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Solving radical equations 3 | Exponent expressions and equations | Algebra I | Khan Academy

Video vocabulary

color

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US / 'kʌlə(r) /

UK / ˈkʌlɚ /

A1
  • noun
  • Quality of things you can see, e.g. red, blue
  • Pink or red in your face, e.g. after being ill
  • The shade of someone's skin e.g. black, or yellow
  • verb
  • To change or affect someone's opinion
  • To make something colorful using colored pencils

not

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US / nɒt /

UK / nɑt /

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

maybe

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US / ˈmeɪbi /

UK / ˈmebi /

A1
  • adverb
  • Possibly but not certainly; perhaps

our

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US / 'aʊə(r) /

UK / aʊr /

A1
  • determiner
  • Belonging to us

whole

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US / həul /

UK / hol /

A1
  • adjecitve
  • Complete or full; all of
  • Being in a good condition
  • noun
  • Complete amount or sum; total

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

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

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

substitute

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US / 'sʌbstɪtju:t /

UK / ˈsʌbstɪˌtut, -ˌtjut /

B2
  • noun
  • A person or thing acting in place of another
  • verb
  • To perform the tasks instead of someone else
  • To replace one person or thing for another

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

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

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

become

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US / bɪ'kʌm /

UK / bɪˈkʌm /

A1
  • verb
  • To begin to be; grow to be; develop into
  • To be suitable for a particular job or role

same

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US / seɪm /

UK / sem /

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

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

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

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

solve

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US / sɒlv /

UK / sɑ:lv /

A2
  • verb
  • To figure out a way to handle a difficult problem

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

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

quadratic

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US / kwɒˈdrætɪk /

UK / kwɑˈdrætɪk /

A1
  • adjecitve
  • Polynomial of the second degree

isolated

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US / ˈaɪsəleɪtɪd /

UK / ˈaɪsəˌletɪd /

B1
  • verb
  • To identify, consider, or deal with separately
  • To keep in a place or situation apart from others
  • To separate something from another substance

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

even

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US / 'i:vn /

UK / ˈivən /

A1
  • adjecitve
  • Being equal in influence, power, possibility etc.
  • Being divided equally or fairly
  • (Of teams/contest) with similar chances of success
  • Smooth, level, or regular
  • Can be divided by 2; ending in 2, 4, 6, 8, or 0
  • At a regular, equally steady manner
  • Remaining steady and unchanging
  • adverb
  • (When this is surprising) as well; too
  • (Used to compare two things/stress the difference)
  • verb
  • To make something level; to flatten
  • To make something equal

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

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’

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

expression

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US / ɪk'spreʃn /

UK / ɪkˈsprɛʃən /

A2
  • noun
  • Act of making your thoughts and feelings known
  • Group of words that have a specific meaning

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

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

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

cancel

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US / 'kænsl /

UK / ˈkænsəl /

A2
  • verb
  • To end a legal, business, or other agreement
  • To stop a planned event from happening

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

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

rewrite

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US / ˌri:'raɪt /

UK / riˈraɪt /

A2
  • verb
  • To write again to improve, or correct errors

both

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US / bəuθ /

UK / boθ /

A1
  • determiner
  • Used to refer to two things at the same time
  • pronoun
  • Used to refer to two things at the same time

add

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US / æd /

UK / æd /

A1
  • verb
  • To include as well
  • To put two things or numbers together, e.g. 2+2

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

original

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US / ə'rɪdʒənl /

UK / əˈrɪdʒənəl /

A2
  • adjecitve
  • Being first made, thought or performed; fresh
  • Being unique or thinking differently from others

here

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US / hɪə(r) /

UK / hɪr /

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

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

already

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US / ɔ:lˈredi /

UK / ɔlˈrɛdi /

A1
  • adverb
  • Having happened or been done before this time

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

side

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US / saɪd /

UK / saɪd /

A1
  • adjecitve
  • In addition to the central or most important thing
  • Next to, or very close to, the right or left of
  • noun
  • Position or opinion that is opposite to another
  • Right or left part of a person's body
  • Feature of someone's personality
  • Straight edge of an object
  • One of two or more groups fighting each other
  • verb
  • To decide to agree with one point, not the other

point

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US / pɔɪnt /

UK / pɔɪnt /

A1
  • noun
  • An item to be discussed
  • Small spot or dot
  • Fact or detail
  • Feature of something
  • The size of the text on a page or screen
  • A certain time or stage in a process
  • Certain position in time or space
  • Idea or fact you try to convince people about
  • Measurement of scores in a game, sport
  • Sharp end of something, e.g. a pen or pin
  • verb
  • To face a certain direction, e.g. north
  • To indicate something with your finger to others

actually

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US / ˈæktʃuəli /

UK / ˈæktʃuəli /

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

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

divide

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US / dɪ'vaɪd /

UK / dɪˈvaɪd /

A2
  • verb
  • To split numbers by another number, e.g. 6 / 2 = 3
  • To separate something into equal pieces

quantity

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US / ˈkwɒntəti /

UK / ˈkwɑntɪti /

A2
  • noun
  • A large amount of something
  • Amount or number of something

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

part

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US / pɑ:t /

UK / pɑ:rt /

A1
  • adjecitve
  • To some degree; half; not fully
  • noun
  • Division of a book
  • Ratio of something, e.g. 3 of gin, 1 of tonic
  • A line in a person's hair, made with a comb
  • Character an actor plays on stage, movie, or TV
  • Some, but not all of a specific thing
  • Role in causing something to happen
  • verb
  • To make a line in a person's hair, by using a comb
  • To move two things apart creating a space
  • To leave someone, or to break off a relationship

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

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)

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

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

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

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

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

clear

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US / klɪə(r) /

UK / klɪr /

A1
  • adjecitve
  • Empty; without anything in it or on it
  • Being certain and without doubt
  • Being without any streaks, spots, or cracks
  • Easy to understand; well-explained; obvious
  • adverb
  • Completely; entirely; through the whole of
  • Away from; free from
  • verb
  • To recover from or remove a problem
  • To get rid of the entire contents of
  • To give permission for something to happen
  • To make a place or surface empty by removing
  • To prove that someone is not guilty or to blame

hand

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US / hænd /

UK / hænd /

A1
  • noun
  • Cards given to a player in a card game
  • Piece of a clock that points to the time
  • Someone who performs physical tasks or work
  • Body part at the end of a person's arm
  • Help for someone performing a particular action
  • Condition of having power or influence
  • Member of the crew of a ship
  • verb
  • To give something to someone personally

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

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

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

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

you

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US / jʊ /

UK / ju /

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

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

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

entire

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US / ɪn'taɪə(r) /

UK / ɛnˈtaɪr /

A2
  • adjecitve
  • Complete or full; with no part left out; whole

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

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

verify

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US / 'verɪfaɪ /

UK / ˈvɛrəˌfaɪ /

B2
  • verb
  • To prove that something is right, accurate or true

solution

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US / səˈlu:ʃn /

UK / səˈluʃən /

A2
  • noun
  • Mix of a liquid and a solid or a gas
  • Way to solve or deal with a problem

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

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

back

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US / bæk /

UK / bæk /

A1
  • adjecitve
  • Farthest from the front e.g. in a classroom
  • adverb
  • Have returned to a place you were before
  • noun
  • The part of a chair that the upper body leans upon
  • Location at the rear of something
  • The reverse of side something
  • Area on the rear of your body
  • verb
  • To bet money on something
  • To go backwards in a car
  • To support and encourage someone or some cause

from

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US / frəm /

UK / frʌm, frɑm,frəm /

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

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

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

ask

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US / ɑ:sk /

UK / æsk /

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

start

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US / stɑ:t /

UK / stɑrt /

A1
  • noun
  • First time or place that a thing exists; beginning
  • First opportunity to achieve something, e.g. a job
  • Sudden action or movement because you are scared
  • other
  • Beginning of something in place or time
  • verb
  • To do, be or happen for the first time; begin
  • To turn something on

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

green

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US / gri:n /

UK / ɡrin /

A1
  • adjecitve
  • Color of young leaves
  • Covered with vegetation, e.g. grass
  • Concerned about protecting the environment
  • The color of young leaves
  • Lacking in experience/knowledge due to being young
  • Being not fully grown or ripe, as in fruit
  • noun
  • Large grassy area
  • used as a part of a name of a place (UK)

equation

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US / ɪˈkweɪʒn /

UK / ɪˈkweʒən, -ʃən /

B1
  • noun
  • Mathematical statement showing things to be equal
  • Complex set of different facts, ideas or issues

definitely

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US / ˈdefɪnətli /

UK / ˈdefɪnətli /

A2
  • adverb
  • Without question; beyond doubt

much

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US / mʌtʃ /

UK / mʌtʃ /

A1
  • adjecitve
  • Very; to a high level or degree
  • adverb
  • A lot; large amount; a high degree of
  • Nearly; basically
  • On many occasions; often
  • noun
  • A large amount; a great quantity

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

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

black

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US / blæk /

UK / blæk /

A1
  • adjecitve
  • Color of the sky on a dark night
  • noun
  • A person with dark skin, often of African origin
  • Person's name
  • verb
  • To fill in something to make it a very dark color

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)

for

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US / fə(r) /

UK / fɔr,fə /

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

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
  • Subtitles section
  • We're asked to solve for x.
  • So we have the square root of the entire quantity 5x squared minus 8 is equal to 2x.
  • Now we already have an expression under a radical isolated, so the easiest first step here is really just to square both sides of this equation.
  • So let's just square both sides of that equation.
  • Now the left-hand side, if you square it, the square root of 5x squared minus 8 squared is going to be 5x squared minus 8.
  • This is 5x squared minus 8.
  • And then the right-hand side, 2x squared is the same thing as 2 squared times x squared or 4x squared.
  • Now we have a quadratic.
  • Now let's see what we can do to maybe simplify this a little bit more.
  • Well, we could subtract 4x squared.
  • Or actually, even better, let's subtract 5x squared from both sides so that we just have all our x terms on the right-hand side.
  • So let's subtract 5x squared from both sides.
  • Subtract 5x squared from both sides of the equation.
  • The left-hand side, this cancels out.
  • That was the whole point.
  • We're just left with negative 8 is equal to 4x squared minus 5x squared, that's negative 1x squared.
  • Or we could just write negative x squared, just like that.
  • And then we could multiply both sides of this equation by negative 1.
  • That'll make it into positive 8.
  • Or I could divide by negative 1, however you want to view it.
  • Negative 1 times that times negative 1.
  • So we get positive 8 is equal to x squared.
  • And now we could take the square root of both sides of this equation.
  • So let's take the square root of both sides of this equation.
  • The principal square root of both sides of this equation.
  • And what do we get?
  • We get, on the right-hand side, x is equal to the square root of 8.
  • And 8 can be rewritten as 2 times 4.
  • And this can be rewritten as the square root of 2 times the square root of 4 is equal to x.
  • I don't like this green color so much.
  • And what's the square root of 4, the principal root of 4?
  • It's 2.
  • So that right there is 2.
  • So this side becomes 2, this 2, times the square root of 2.
  • And that is equal to x.
  • Now let's verify that this is the solution to our original equation.
  • So let's substitute this in, first to the left-hand side.
  • So on the left-hand side, we have 5 times 2 square roots of 2 squared minus 8.
  • And then we're going to have to take the square root of that whole thing.
  • So this is going to be equal to-- we're just focused on the left-hand side right now.
  • This is equal to the square root of 5 times 2 squared, which is 4, times the square root of 2 squared, which is 2.
  • And then minus 8.
  • And this is 5 times 4 is 20 times 2 is 40.
  • And then you have 40 minus 8 is 32.
  • So this is equal to the square root of 32.
  • Square root of 32 is the same thing as the square root of 16 times 2.
  • The square root of 16 is 4.
  • So this is the same thing as the square root of 16 times the square root of 2.
  • Or 4 square roots of 2.
  • So that's what the left hand simplifies to when we-- and remember, the original equation didn't have these squares here, so if you just look at the green part, the green part on the left-hand side just simplified to 4 roots of 2.
  • Let's see what 2x simplifies to.
  • Our original right-hand side was just the 2x.
  • That's parentheses with the square added later.
  • So what's 2x?
  • 2 times 2 roots of 2.
  • 2 square root of 2.
  • Well that's just 4 square root of 2.
  • So when x is equal to 2 square roots of 2, the left-hand side equals 4 square roots of 2.
  • And remember, the left-hand side looked like this when we started off.
  • The left-hand side when we started off didn't have that there.
  • I want to make that clear.
  • So when you substitute this back into this left-hand side, you get 4 square roots of 2.
  • When you substitute it back into the original right-hand side, you get 4 square roots of 2.
  • So it's definitely the right-- I'm trying to write in black.
  • It's definitely the right solution.