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Subtracting and simplifying radicals | Exponent expressions and equations | Algebra I | Khan Academy

Video vocabulary

will

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US / wɪl /

UK / wɪl /

A1
  • noun
  • Desire or choice of someone
  • Document saying who gets your money when you die
  • Strong desire to do something; determination
  • Desire to do something; strong wish to do
  • other
  • Used with verbs to express the future
  • verb
  • To leave property to someone after your death
  • To use mental effort to make something happen
  • Am (is, are) likely to do
  • To influence someone to do something
  • To make something happen by strongly wanting it

straight

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US / streɪt /

UK / stret /

A2
  • adjecitve
  • Not having curves, bends, or angles
  • Not gay; heterosexual
  • honest and direct
  • adverb
  • in a line; immediately; honestly and directly

probably

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US / ˈprɒbəbli /

UK / ˈprɑbəbli /

A1
  • adverb
  • That is likely to happen or be true

try

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US / traɪ /

UK / traɪ /

A1
  • noun
  • Act of putting the ball over the rugby goal line
  • verb
  • To make an effort, to attempt to do something
  • To examine someone or something in a court of law
  • To test to see if it is good or you like it
  • To make a person go through hardship; test
  • To examine something to see if it works

stick

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US / stɪk /

UK / stɪk /

A2
  • noun
  • Long thin piece of wood from a tree
  • verb
  • To push a sharp or pointed object into something
  • To join together using glue or paste
  • To remain in one place or position for a long time

four

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US / fɔ:(r) /

UK / fɔr, for /

A1
  • number
  • 4

should

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US / ʃʊd /

UK / ʃʊd /

A1
  • other
  • Used to indicate what is proper or reasonable

convenient

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US / kənˈvi:niənt /

UK / kənˈvinjənt /

A2
  • adjecitve
  • Allowing you to do something with less trouble

rid

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US / rɪd /

UK / rɪd /

A2
  • verb
  • To cause to no longer have (pest, problem)

exactly

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US / ɪgˈzæktli /

UK / ɪɡˈzæktli /

A1
  • adverb
  • No more and no less than; precisely

third

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US / θɜ:d /

UK / θɜ:rd /

A1
  • adjecitve
  • 3rd: Number after second

daunt

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US / dɔ:nt /

UK / dɔnt, dɑnt /

B2
  • verb
  • To make someone feel less courageous or confident

actually

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US / ˈæktʃuəli /

UK / ˈæktʃuəli /

A1
  • adverb
  • Used to add new (often different) information

inside

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US / ˌɪn'saɪd /

UK / ɪnˈsaɪd, ˈɪnˌsaɪd /

A2
  • adjecitve
  • Being in something
  • Being in a building
  • adverb
  • Into a house; indoors
  • noun
  • Inner part or surface of something

write

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US / raɪt /

UK / raɪt /

A1
  • verb
  • To compose letters and words on paper or a screen
  • To invent or create a computer program
  • To create a song or piece of music

realize

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US / 'ri:əlaɪz /

UK / ˈriəˌlaɪz /

A1
  • verb
  • To become aware of or understand mentally

here

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US / hɪə(r) /

UK / hɪr /

A1
  • adverb
  • In this place; at this location, position or time

use

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US / ju:s /

UK / ju:s /

A1
  • noun
  • Ability to employ something
  • Need to enable it to work
  • Permission to do something with something
  • Act of spending money
  • Operation of a machine for its function
  • verb
  • To have; to eat, drink, consume etc.
  • To need to operate or work
  • To operate a machine, e.g. a computer
  • To treat a person badly
  • To do something with, for a task or purpose

time

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US / taɪm /

UK / taɪm /

A1
  • noun
  • Speed at which music is played; tempo
  • Point as shown on a clock, e.g. 3 p.m
  • Number of hours, minutes needed to do something
  • Occasion when something happens
  • Period or occasion that something occurred
  • Period in history or the past
  • Something measured in minutes, hours, days, etc.
  • How long an event takes; duration
  • verb
  • To check speed at which music is performed
  • To choose a specific moment to do something
  • To measure how long an event takes, e.g. a race
  • To schedule something to occur at a specific moment

exact

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US / ɪɡ'zækt /

UK / ɪɡˈzækt /

A2
  • adjecitve
  • Completely correct; accurate; specific
  • verb
  • To get something, sometimes using force

restrict

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US / rɪ'strɪkt /

UK / rɪˈstrɪkt /

A2
  • verb
  • To prevent a person from doing something

messy

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US / 'mesɪ /

UK / ˈmɛsi /

A2
  • adjecitve
  • Being complex or difficult to fix
  • Being untidy or dirty

for

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US / fə(r) /

UK / fɔr,fə /

A1
  • preposition
  • Used to show the purpose, or need of something

necessarily

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US / ˌnesəˈserəli /

UK / ˌnɛsɪˈsɛrəli, -ˈsɛr- /

A2
  • adverb
  • In a way that is needed/required/is unavoidable

ask

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US / ɑ:sk /

UK / æsk /

A1
  • verb
  • To say to someone that you want something

positive

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US / ˈpɒzətɪv /

UK / ˈpɑzɪtɪv /

A2
  • adjecitve
  • Showing agreement or support for something
  • Being sure about something; knowing the truth
  • Having the charge produced by electrons
  • Being good or useful
  • Showing that a chemical is present in a test

define

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US / dɪ'faɪn /

UK / dɪˈfaɪn /

A2
  • verb
  • To explain the meaning of words
  • To set or mark the limits of something

explicitly

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US / ɪk'splɪsɪtlɪ /

UK / ɪk'splɪsɪtlɪ /

B1
  • adverb
  • Clearly; specifically

fully

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US / 'fʊlɪ /

UK / ˈfʊli /

A1
  • adverb
  • Completely or entirely

under

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US / ˈʌndə(r) /

UK / ˈʌndɚ /

A1
  • adjecitve
  • In the same place as another thing, but lower
  • adverb
  • In a lower quantity or price than expected
  • preposition
  • According to the terms of an agreement or law
  • Managed or controlled by the authority of
  • Being of a lesser quality or amount than expected
  • Influenced or affected by something or someone
  • Less or lower in age, amount, size or number

well

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US / wel /

UK / wɛl /

A1
  • adjecitve
  • Being in a fortunate, good condition or state
  • Healthy and in good condition
  • adverb
  • In an acceptable, proper, or successful manner
  • In a complete, total, or full manner
  • A great and considerable degree
  • In a successful way, in a good or satisfactory way
  • exclamation
  • Used to begin or continue a particular statement
  • Used to show you want to start saying something
  • Used to express that you are waiting for a reply
  • You say this to change the topic of a conversation
  • Used to indicate you are making a final remark
  • noun
  • Long deep hole in the ground to get water
  • verb
  • To cause your eyes to fill with tears

just

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US / dʒʌst /

UK / dʒʌst /

A1
  • adjecitve
  • Proper or appropriate; as is deserved
  • Doing or being what is right or fair
  • Legally correct; having enough evidence
  • adverb
  • Almost; nearly
  • Exactly at the time of
  • Exactly (the same as, like)

logic

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US / ˈlɒdʒɪk /

UK / ˈlɑ:dʒɪk /

A2
  • noun
  • Proper, valid sensible reasoning
  • Scientific study of reasoning

myself

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US / maɪˈself /

UK / maɪˈsɛlf /

A1
  • pronoun
  • The same person who did the action mentioned
  • My regular, usual, or healthy self

negative

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US / 'neɡətɪv /

UK / ˈnɛɡətɪv /

A2
  • adjecitve
  • Being harmful, unwanted or unhelpful
  • In mathematics, being less than zero
  • Focusing on the bad aspects; pessimistic
  • noun
  • The opposite to a positive electrical charge
  • In grammar, containing words such as 'no' or 'not'
  • Reply to a question or statement that means 'no'
  • Image on camera film used to make a photo

careful

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US / ˈkeəfl /

UK / ˈkerfl /

A2
  • adjecitve
  • Trying not to make mistakes; working slowly

break

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US / breɪk /

UK / brek /

A1
  • noun
  • Time you stop an activity before continuing
  • End of a relationship
  • An escape from a place such as a jail
  • (Lucky) advantage or benefit from something
  • Find a solution or answer to a problem or crime
  • Change in the weather
  • verb
  • To create a new record e.g. running the 100m dash
  • To form a crack in something
  • To burst or become damaged
  • To end a relationship
  • To escape from a place such as a jail
  • To train a wild animal e.g. a horse
  • To separate into pieces by force, or by dropping
  • To act against a law, rule, or promise
  • To become known suddenly, as in the news
  • To not do what you promised e.g. not keep promises
  • To solve a crime, or answer a problem
  • To stop functioning properly
  • To suddenly start, open or commence
  • To change in pitch suddenly, as in a voice
  • To fall on the shore, as in waves
  • To begin or change suddenly; the dawn or weather
  • To defeat by causing the person to lose their will

prime

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US / praɪm /

UK / praɪm /

A2
  • adjecitve
  • Concerning the highest in quality or value
  • Concerning the highest level of achievement
  • Most important, chief importance in value
  • verb
  • To get a person ready for; prepare someone
  • To coat with paint to prepare it for the main coat

with

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US / wɪð /

UK / wɪð, wɪθ /

A1
  • preposition
  • As an employee of a certain company
  • Against something or someone
  • By using something as a means
  • Due to; because of
  • Including
  • Possessing as a feature
  • Related to
  • (Of the manner/attitude by which you do something)
  • Used to express that people or things are together

focus

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US / 'fəʊkəs /

UK / ˈfokəs /

A2
  • noun
  • Main purpose or center of interest or activity
  • verb
  • To see clearly by adjusting your eyes or a camera
  • To keep your attention, concentration on one thing

could

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US / kəd /

UK / kʊd /

A1
  • other
  • Past form of 'can' to mean have ability
  • Used to ask for something politely, or to offer

have

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US / həv /

UK / hæv /

A1
  • verb
  • To drink, smoke, eat or use something
  • To experience the effects of something
  • To organize an event, or join in an activity
  • To own, possess, or hold something
  • To cause to happen or produce a particular effect

see

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US / si: /

UK / si /

A1
  • verb
  • To go on a date with someone
  • To predict whether something is, or will be true
  • To understand what someone says
  • To use your eyes to look at something
  • To visit a place often for sightseeing or pleasure
  • To visit or meet with someone
  • To find out by waiting or looking
  • To watch (a game, movie or TV show)

remember

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US / rɪ'membə(r) /

UK / rɪˈmɛmbɚ /

A1
  • verb
  • To give someone a gift, e.g. birthday, wedding
  • To hold a thought in your mind to not forget it
  • To bring a previous image or idea to your mind

away

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US / ə'weɪ /

UK / əˈwe /

A1
  • adjecitve
  • Not present
  • adverb
  • Disappear completely
  • Doing something with a lot of energy
  • Not here; far from here; in a different direction
  • To a different area, location

radical

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US / ˈrædɪkl /

UK / ˈrædɪkəl,'rædɪkḷ /

B1
  • adjecitve
  • Very new and different from what is traditional
  • Concerning something's most basic part or form
  • noun
  • Person who believes in extreme political change

one

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US / wʌn /

UK / wʌn /

A1
  • pronoun
  • You; we; people in general; someone
  • The thing or person previously referred to
  • adjecitve
  • Used to refer to people generally
  • Being a strong example of (something mentioned)
  • number
  • Number 1

term

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US / tɜ:m /

UK / tɚm /

A1
  • noun
  • Conditions applying to an agreement, contract
  • Length of time something is expected to happen
  • Fixed period of weeks for learning at school
  • The (precise) name given to something
  • verb
  • To call; give a name to

the

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US / ðə /

UK / ðə /

A1
  • article
  • Used to refer to something already mentioned
  • Used to show there is only one of something
  • determiner
  • Used to describe all of a family

let

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US / let /

UK / lɛt /

A1
  • verb
  • To allow someone to do something
  • Introducing a suggestion to do something together
  • To rent a house, etc. to others

power

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US / 'paʊə(r) /

UK / ˈpaʊɚ /

A1
  • noun
  • Legal or official right to perform certain actions
  • Ability to move forcefully and quickly
  • Energy of something (e.g. electricity or fuel)
  • Mathematical way to multiply a number
  • Condition of being in political control
  • Physical force, energy, and strength
  • verb
  • To give energy to something, e.g. by electricity
  • To move something forcefully and quickly

this

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US / ðɪs /

UK / ðɪs /

A1
  • adjecitve
  • Used to indicate something already been discussed
  • Used to indicate something happening around now
  • adverb
  • An indication by a physical motion or gesture
  • A specific amount of
  • determiner
  • Person, thing, or idea near you
  • pronoun
  • Person, thing that has already been discussed

although

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US / ɔ:lˈðəu /

UK / ɔlˈðo /

A1
  • conjunction
  • Despite the fact that; however

perfect

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US / 'pɜ:fɪkt /

UK / ˈpɚfɪkt /

A1
  • adjecitve
  • So good it cannot be improved
  • verb
  • To do something so well, it cannot be done better

make

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US / meɪk /

UK / mek /

A1
  • noun
  • Product made by a particular company; brand
  • verb
  • To arrange or prepare something e.g. dinner
  • To get to (a place) on time
  • To gain the status of (teacher, lawyer, etc.)
  • To create something by putting things together
  • To earn a certain amount of money at a job
  • To cause or force a person to do something
  • To cause something to happen or be formed

root

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US / ru:t /

UK / rut, rʊt /

A2
  • noun
  • Emotional connection with a place, history etc.
  • The origin or starting place of something
  • A number that is multiplied by itself
  • Part of plant growing underground, as to get water
  • Part of tooth, hair etc. from which the rest grows
  • Base part of a word to which affixes can be added
  • verb
  • To cause a plant to develop or grow roots
  • (Animals) to search for e.g. food in earth
  • To stop someone moving, as through fear

into

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US / 'ɪntə /

UK / ˈɪntu /

A1
  • preposition
  • Moving or going inside something
  • In the same direction as; in the direction of
  • So as to become; taking the state of

assumption

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US / ə'sʌmpʃn /

UK / əˈsʌmpʃən /

A2
  • noun
  • Something you believe to be so, but aren't sure of

coefficient

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US / ˌkəʊɪˈfɪʃnt /

UK / ˌkoʊɪˈfɪʃnt /

B2
  • adjecitve
  • Number by which another number is multiplied

you

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US / jʊ /

UK / ju /

A1
  • pronoun
  • Person someone is speaking or writing to
  • Person or people in general

little

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US / 'lɪtl /

UK / ˈlɪtl /

A1
  • adjecitve
  • Being short in length of time
  • Not great in size, amount, or degree; small
  • Being very young or younger than others
  • adverb
  • By an amount or degree that is not very much
  • Not often; rarely
  • noun
  • A person's name

how

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US / haʊ /

UK / haʊ /

A1
  • adjecitve
  • To what degree? in what amount?
  • adverb
  • (Used to explain the way to do something)
  • exclamation
  • For what purpose or reason?
  • (Used to ask someone or something's condition)

than

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US / ðən /

UK / ðən /

A1
  • conjunction
  • Used to compare two things that are not equal

fourth

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US / fɔ:θ /

UK / fɔ:rθ /

A1
  • noun
  • 4th

subtract

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US / səbˈtrækt /

UK / səbˈtrækt /

B2
  • other
  • To take away a value or amount from another
  • verb
  • To take away a value or amount from another

everything

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US / 'evrɪθɪŋ /

UK / ˈɛvriˌθɪŋ /

A1
  • pronoun
  • All of the things mentioned

look

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US / lʊk /

UK / lʊk /

A1
  • noun
  • Person's beauty or physical attractiveness
  • Particular style of dress, clothes, or appearance
  • The way someone, something appears to be
  • Act of searching for or examining something
  • verb
  • To appear to be; seem

all

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US / ɔ:l /

UK / ɔl /

A1
  • adverb
  • Completely; totally
  • determiner
  • Being every one of something
  • pronoun
  • 100% of something; the complete amount

they

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US / ðeɪ /

UK / ðe /

A1
  • pronoun
  • Two or more people, animals, or things

pretty

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US / 'prɪtɪ /

UK / ˈprɪti /

A1
  • adjecitve
  • Being attractive to the eye in a simple way
  • adverb
  • Very; to a great degree

regular

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US / ˈregjələ(r) /

UK / ˈrɛɡjəlɚ /

A2
  • adjecitve
  • Having an equal amount of space or time in between
  • Occurring or being done frequently
  • Being normal, usual, or average
  • noun
  • Customers who frequently visit a place
  • Soldier who has a permanent job in the army

their

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US / ðɛː /

UK / ðer /

A1
  • determiner
  • Belonging to them

bit

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US / bɪt /

UK / bɪt /

A1
  • noun
  • Device put in a horse's mouth to control it
  • Small piece of something
  • verb
  • (E.g. of fish) to take bait and be caught

take

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US / teɪk /

UK / tek /

A1
  • noun
  • Filming of a single scene for TV or the movies
  • verb
  • To accept something that is offered
  • To use a method of traveling, e.g. a bus or train
  • To use a camera to make (a photo)
  • To pick up something and go away with it
  • To study a subject in school
  • To attempt to pass (an exam)
  • To require a certain amount of time, money, space

multiply

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US / ˈmʌltɪplaɪ /

UK / ˈmʌltəˌplaɪ /

B1
  • verb
  • To increase in number by reproducing/having babies
  • To increase something by a large quantity
  • To have increased by a large quantity
  • To calculate two numbers e.g. 2 x 4

over

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US / 'əʊvə(r) /

UK / ˈovɚ /

A1
  • adverb
  • Finished; no longer happening
  • Towards the ground/away from a standing position
  • noun
  • A set of six consecutive balls bowled in cricket
  • other
  • Finished
  • preposition
  • Showing the relation when a thing is above another
  • On or covering something
  • Above or across something
  • More than you need
  • From one side to the other
  • In the direction of; toward

leave

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US / li:v /

UK / liv /

A1
  • noun
  • Permission to do something
  • Vacation time; time off work
  • verb
  • To go away from; depart
  • To gift property to someone after you die
  • To allow something to continue happening
  • To let something remain unused or available
  • To let something or someone remain somewhere

real

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US / rɪəl /

UK / ˈriəl, ril /

A1
  • adjecitve
  • Actually existing or happening, not imagined
  • Being important or special

and

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US / ənd /

UK / ənd, ən,ænd /

A1
  • conjunction
  • Used to refer to two or more things
  • Plus; in addition; on top of that
  • Used to introduce an action that follows another

front

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US / frʌnt /

UK / frʌnt /

A1
  • adjecitve
  • Opposite of back; the forward part of an object
  • noun
  • Behavior not showing a person's true feelings
  • Area where fighting in a war is happening
  • Place where air of different temperatures meets
  • verb
  • To have the forward part facing something
  • To lead a group of people, usually a band

version

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US / ˈvə:ʃən /

UK / ˈvɚʒən, -ʃən /

A2
  • noun
  • Different way that someone interprets something
  • New or different form of something
  • An updated form of some software

out

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US / aʊt /

UK / aʊt /

A1
  • adverb
  • No longer stylish (e.g. fashion)
  • Away from home, business, or the usual place
  • In a direction/movement away from inside or center
  • noun
  • Act when a batter cannot continue playing
  • verb
  • To tell people a secret

something

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US / ˈsʌmθɪŋ /

UK / ˈsʌmθɪŋ /

A1
  • adverb
  • In some degree or measure
  • noun
  • a person or thing of some value or consequence
  • pronoun
  • Thing that is not yet known or named
  • Approximately

lemon

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US / 'lemən /

UK / ˈlɛmən /

B2
  • noun
  • Badly made or poorly functioning product
  • Small yellow fruit with sour juice

two

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US / tu: /

UK / tu /

A1
  • number
  • 2

from

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US / frəm /

UK / frʌm, frɑm,frəm /

A1
  • preposition
  • Starting at a particular place, time or level

minus

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US / ˈmaɪnəs /

UK / ˈmaɪnəs /

A2
  • adjecitve
  • Being close to the bottom of a letter grade
  • noun
  • Negative quality; disadvantage
  • Sign that indicates subtraction
  • preposition
  • Being less than zero in number
  • Used when subtracting one number from another
  • verb
  • To take one number away from another; subtract

any

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US / 'enɪ /

UK / ˈɛni /

A1
  • adjecitve
  • One, or some, no matter which
  • pronoun
  • One (thing) of many; some

square

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US / skweə(r) /

UK / skwɛr /

A2
  • adjecitve
  • Being fair or honest
  • Multiply a number by itself e.g. 2x2 or 6x6
  • noun
  • Shape with 4 equal length sides and 4 equal angles
  • The result of multiplying Length by the width
  • Open public area in the middle of the town
  • verb
  • To make something balance or be equal
  • To multiply a number by itself, e.g. 2x2 or 6x8
  • To straighten the edge to form a four-sided shape

case

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US / keɪs /

UK / kes /

A1
  • noun
  • Container used to carry things, e.g. clothes
  • Set of facts about a crime
  • Set of facts about an event
  • Example or instance of something
  • verb
  • To find out about a place, as in planning to steal

value

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US / 'vælju: /

UK / ˈvælju /

A1
  • noun
  • Importance you attach to something
  • Some information expressed as a number
  • Stated price of something; worth
  • verb
  • To place a high importance on something
  • To say how much money something is worth

great

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US / ɡreɪt /

UK / ɡret /

A1
  • adjecitve
  • Very large in size
  • Very important
  • Very good; fantastic; wonderful
  • adverb
  • Very good; better than before
  • noun
  • Successful and well-admired person

number

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US / ˈnʌmbə(r) /

UK / ˈnʌmbɚ /

A1
  • noun
  • Symbols such as 1, 2, 56, 793
  • Particular song or dance performed during a show
  • Total quantity or amount of things
  • verb
  • To put numbers on things
  • To assign a sequence within a group, series, set
  • To claim to be part of a larger group, series, set

remind

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US / rɪ'maɪnd /

UK / rɪˈmaɪnd /

A2
  • verb
  • To cause someone to remember what they forgot

right

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US / raɪt /

UK / raɪt /

A1
  • adjecitve
  • Correct or true
  • The south side of you looking at the rising sun
  • adverb
  • Exactly in a place or time
  • Being appropriate for a particular event
  • In a straight or direct manner
  • noun
  • Something you are legally or morally allowed to do
  • Ideal of what is just and good
  • Political view based on conservatism
  • verb
  • To fix something previously wrong or unjust
  • To make upright, as a boat that has turned over

then

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US / ðen /

UK / ðɛn /

A1
  • adverb
  • A time that is not now
  • Following another thing in time or arrangement
  • Following on reasonably from what was just stated
  • At that time, not now

first

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US / fɜ:st /

UK / fɚst /

A1
  • adjecitve
  • 1st; Coming before all others in time or place
  • noun
  • Something that has not happened before
  • Position of the winner of a competition

example

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US / ɪgˈzɑ:mpl /

UK / ɪɡˈzæmpəl /

A1
  • noun
  • Thing, person which represents a category

absolute

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US / ˈæbsəlu:t /

UK / ˈæbsəˌlut /

A2
  • adjecitve
  • Complete; total; pure; not limited in any way
  • noun
  • Something that is complete, total, pure, certain

get

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US / ɡet /

UK / ɡɛt /

A1
  • verb
  • To become affected by illness or disease
  • To begin to feel or understand an emotion or idea
  • To send or bring someone or something home, etc.
  • To go somewhere to obtain something
  • To (cause to) do a particular thing
  • To obtain, receive or be given something
  • To currently have
  • To prepare for use
  • To understand something being said or read

what

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US / wɒt /

UK / hwɑt, hwʌt, wɔt, wʌt,hwət, wət /

A1
  • pronoun
  • Thing or things that; the same kind as
  • Used to emphasize something you are about to say
  • adjecitve
  • Used to refer to a particular amount, or number
  • Used to place emphasis on a particular quality
  • adverb
  • To a certain degree
  • determiner
  • Question words used for asking for information
  • exclamation
  • Used to express excitement, shock, or surprise
  • Used to ask people to repeat something they said

straightforward

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US / ˌstreɪtˈfɔ:wəd /

UK / stretˈfɔrwəd /

B1
  • adjecitve
  • Easy to do or understand; not complicated

that

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US / ðæt /

UK / ðæt, ðət /

A1
  • adjecitve
  • The person or thing being talked about
  • Used to identify something both the speakers know
  • adverb
  • Used to reinforce adjectives and adverbs
  • To such a degree
  • conjunction
  • Used to connect a noun clause
  • Used to introduce an adverbial clause
  • Used to introduce a noun clause
  • determiner
  • Used as a noun to refer to something
  • pronoun
  • Referring an object far away
  • Used to refer to the relative pronoun ‘which’

least

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US / li:st /

UK / list /

A1
  • adverb
  • In the smallest or lowest way
  • noun
  • Something that is of the lowest or smallest degree

like

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US / laɪk /

UK / laɪk /

A1
  • adjecitve
  • Being equal in status or kind to something else
  • Similar; the same
  • adverb
  • For example
  • preposition
  • Used as a filler; used to ad emphasis
  • In a way similar to the way something is done
  • Such as; for example
  • verb
  • To want to
  • To find something pleasing; to prefer something

skip

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US / skɪp /

UK / skɪp /

B2
  • noun
  • Very large waste disposal bin
  • verb
  • To move forward by taking fast steps and jumps
  • To not do something expected or required
  • To move rapidly, from one topic to another

step

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US / step /

UK / stɛp /

A1
  • noun
  • Movement done as part of a particular dance
  • Distance covered by one movement of a leg; stride
  • One part or stage in a process
  • Sound made by the feet while walking; footstep
  • Flat horizontal piece that forms stairs
  • verb
  • To raise and moving the foot to put it down

would

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US / wʊd /

UK / wʊd /

A1
  • other
  • Used to indicate something imagined
  • Used to ask or request something politely
  • Verb used to indicate possibility, request etc.
  • Used to indicate a preference
  • Used to indicate a reaction
  • Indicates something that occurred repeatedly
  • Used to indicate willingness or ability to do

deal

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US / di:l /

UK / dil /

A1
  • verb
  • To cope with something - usually troubles
  • To give (something bad e.g. news) to
  • To buy and sell illegal drugs
  • To give out (cards, etc.) to; distribute
  • To do business with someone or to sell products

yellow

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US / ˈjeləʊ /

UK / ˈjeloʊ /

A1
  • adjecitve
  • Color of lemons or the sun
  • Lacking in courage; cowardly (used as an INSULT)
  • verb
  • To turn yellow, often due to being old

pattern

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US / 'pætn /

UK / ˈpætən /

A2
  • noun
  • Model to follow in making or doing something
  • Colors or shapes which are repeated on objects
  • Regular repeated behavior
  • verb
  • To copy the way something else is made

maybe

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US / ˈmeɪbi /

UK / ˈmebi /

A1
  • adverb
  • Possibly but not certainly; perhaps

equal

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US / 'i:kwəl /

UK / ˈikwəl /

A1
  • adjecitve
  • Same in shape, size, or number
  • verb
  • To add up or be the same as

not

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US / nɒt /

UK / nɑt /

A1
  • adverb
  • Word indicating the negative
  • (Used to form the negative of verbs)

want

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US / wɔnt /

UK / wɑnt, wɔnt /

A1
  • noun
  • Something you desire or wish for
  • State or condition of poverty
  • verb
  • To desire or wish for something; hope for a thing

fifth

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US / fɪfθ /

UK / fɪfθ /

A1
  • noun
  • 5th

factorization

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US / ˌfæktəraɪˈzeɪʃən /

UK / ˌfæktərəˈzeɪʃən /

A1
  • noun
  • Resolution of an entity into factors such that when multiplied together they give the original entit

principal

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US / ˈprɪnsəpl /

UK / ˈprɪnsəpəl /

A2
  • adjecitve
  • Being the main or most important
  • noun
  • Leading person in a group of musicians or dancers
  • Head teacher of a school
  • Original amount of money borrowed

now

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US / naʊ /

UK / naʊ /

A1
  • adverb
  • At the present time or moment
  • Right away or in the next possible moment
  • Used to refer to something that just happened
  • Time between the present and a moment in the past
  • conjunction
  • Resulting from or because of something

craziness

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US / 'kreɪzɪnəs /

UK / 'kreɪzɪnəs /

B2
  • noun
  • Insanity; strangeness

really

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US / ˈri:əli /

UK / ˈriəˌli, ˈrili /

A1
  • adverb
  • Used to stress something that is said; definitely
  • In a true or accurate manner
  • Very

same

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US / seɪm /

UK / sem /

A1
  • adjecitve
  • Being equal in quality and amount
  • Identical; not different
  • Not changing; constant

but

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US / bət /

UK / bʌt,bət /

A1
  • conjunction
  • Used before you say something different, opposite

can

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US / kæn /

UK / kən,kæn /

A1
  • noun
  • A metal container for storing food
  • other
  • Able to; have the skill to; have the time to
  • verb
  • To have permission to
  • To be possible to do
  • To preserve food by sealing it in a metal container

imaginary

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US / ɪ'mædʒɪnərɪ /

UK / ɪˈmædʒəˌnɛri /

A2
  • adjecitve
  • Not real; existing only in your imagination
  • Subtitles section
  • We're asked to subtract all of this craziness over here.
  • And it looks daunting.
  • But if we really just focus, it actually should be pretty straightforward to subtract and simplify this thing.
  • Because right from the get-go, I have 4 times the fourth root of 81x to the fifth.
  • And from that, I want to subtract 2 times the fourth root of 81x to the fifth.
  • And so you really can just say, look, I have four of something.
  • And then the something I'll just circle in yellow.
  • I have four of this-- it could be lemons.
  • I have four of these things, and I want to subtract two of these things.
  • These are the exact same things.
  • They're the fourth root of 81x to the fifth.
  • So if I have four lemons and I want to subtract two lemons, I'm going to have two lemons left over.
  • Or if I have four of this thing, and I take away two of this thing, I'm going to have two of these things left over.
  • So these terms right over here simplify to 2 times the fourth root of 81x to the fifth.
  • And I got this 2 just by subtracting the coefficients.
  • Four of something minus two of something is equal to two of that something.
  • And then that, of course, we still have this minus the regular principal square root of x to the third.
  • Now I want to try to simplify what's inside of these under the radical sign so that we can, in this example, actually take the fourth root, and over here actually take, maybe, a principal square root.
  • So first of all, let's see if 81 is something to the fourth power, or at least could be factored into something that is a something to the fourth power.
  • So 81, if we do prime factorization, is 3 times 27.
  • 27 is 3 times 9.
  • And 9 is 3 times 3.
  • So 81 is exactly 3 times 3 times 3 times 3.
  • So 81 actually is 3 to the fourth power, which is convenient because we're going to be taking the fourth root of that.
  • And then x to the fifth we can write as a product.
  • Let me write it over here so it doesn't get messy.
  • So I'm going to write what's under the radical as 3 to the fourth power times x to the fourth power times x.
  • x to the fourth times x is x to the fifth power.
  • And I'm taking the fourth root of all of this.
  • And taking the fourth root of all of this-- that's the same thing as taking the fourth root of this, as taking the fourth root of this.
  • And I'm going to want to skip steps.
  • So I'm taking the fourth root of all of it right over there.
  • And of course, I have a 2 out front.
  • And then x to the third could be written as x squared times x.
  • So it's minus the principal square root of x squared times x.
  • And I broke it up like this because this right over here is a perfect square.
  • Now, how can we simplify this a little bit?
  • And you're probably getting used to the pattern.
  • This is the same thing as the fourth root of 3 to the fourth, times the fourth root of x to the fourth, times the fourth root of x.
  • So let's just skip straight to that.
  • So what is the fourth root?
  • I could write it-- let me write it explicitly, although you wouldn't have to necessarily do this.
  • This is the same thing as the fourth root of 3 to the fourth, times the fourth root of x to the fourth, times the fourth root of x.
  • And 2 is being multiplied times all of that.
  • And then this over here is minus the principal square root of x squared, times the principal square root of x.
  • And so if we try to simplify it, the fourth root of 3 to the fourth power is just 3.
  • So we get a 3 there.
  • The fourth root of x to the fourth power is just going to be x.
  • Actually, I just reminded myself, we have to be careful there.
  • It is not just x, because what if x is negative?
  • If x is negative, then x to the fourth power is going to be a positive value.
  • And when you take the fourth-- remember, this is the fourth principal root-- you're going to get the positive version of x.
  • Or really, you're going to get the absolute value of x.
  • So here, you're going to be getting the absolute value of x.
  • Although, well, you could make an argument that x needs to be positive if this thing is going to be well-defined in the real numbers, because then what's under the radical has to be positive.
  • But let's just go with this for right now.
  • And then we have the fourth root of x.
  • And then over here, the principal square root of x squared, by the same logic, is going to be the absolute value of x.
  • And then this is just the principal square root of x.
  • So let's multiply everything out.
  • We have 2 times 3 times the absolute value of x.
  • So 2 times 3 is 6, times the absolute value of x, times the principal fourth root of x, I should say, minus we took out the absolute value of x, times the principal root of x.
  • And we can't do any more subtracting.
  • Just because you have to realize this is a fourth root.
  • This is a regular square root, principal square root.
  • If these were the same root, then maybe we could simplify this a little bit more.
  • And so then we are all done.
  • And we have fully simplified it.
  • And if you make the assumption that this is defined for real numbers.
  • So that the domain over here, what has to be under these radicals, has to be positive, actually, in every one of these cases.
  • And if they need to be positive, we're not going to be dealing with imaginary numbers.
  • All of these need to be positive.
  • Their domains are x has to be greater than or equal to 0, then you could assume that the absolute value of x is the same as x.
  • But I'll just stick it right here.
  • If you restrict the domain, you could get rid of the absolute value signs.