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OPERATIONS WITH ROOTS

MATH 8

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Review Simplifying Roots

 

 

 

 

3

 

 

 

 

 

6

 

 

 

 

5

7

 

Try and find the BEST factor tree

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Rules for Adding and Subtracting Roots

Simplify all radicals completely

Add and subtract coefficients in front of similar radicals

(Combine like terms, if roots are the same)

Answers may be an expression

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Simplify the expression

 

 

 

 

 

 

 

 

 

Use the coefficients

Keep the square root as is

Did not simplify

because the

square roots are

different

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Simplify the expression

 

 

 

 

 

 

 

 

 

 

Did not simplify

Did not simplify

Did not simplify

same root can combine

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Simplify the expression

 

 

 

 

 

 

 

 

 

 

 

 

2

5

 

4

 

 

2

3

 

 

 

Combine when roots are same

Combine

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Simplify the expression

 

 

 

 

 

 

2

 

3

 

 

All roots are same so they can combine using just the coefficients

Same as this

←

 

 

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Simplify the expression

 

 

 

 

 

 

2

 

3

 

 

 

 

 

 

2

 

 

Combine and place roots in order from least to greatest

Did not simplify

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Rules for Multiplying Roots

Different than

addition and subtraction

Remember

then Check to see if the radical can simplify!

All whole numbers outside the radical can multiply

All numbers under the radical can multiply

OR

factor each radical and simplify by pairing

because of Commutative Property

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Simplify the expression

 

 

 

 

 

 

 

Did not simplify

Does not simplify further

 

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Simplify the expression- two methods

 

 

 

 

 

2

 

 

 

 

 

2

 

equal radicals can multiply

to make a whole number!

OR

Factor each

radical first

Same result, but this method avoids getting

a large number at the beginning that you

are required to break down again

Multiply

leftover

roots

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Simplify the expression

 

 

 

 

 

 

 

2

 

 

 

 

7

 

 

3

3

2

 

 

Big number, it’s easier

to factor and pair

Big number, it’s easier

to factor and pair

Multiply All Whole Numbers, leftover roots stay under the radical

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Simplify the expression

 

 

 

 

 

 

2

 

 

 

 

4

 

3

2

Big number, it’s easier

to factor and pair

Multiply All Whole Numbers, leftover roots stay under the radical

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Rules for Dividing Roots

Different than

add, subtract, or multiply

Remember

OR

factor numerator and denominator

then cancel equal factors

All whole numbers outside the radical can divide

All numbers under the radical can divide

then Check to see if the radical can simplify!

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Simplify the expression

 

 

 

 

 

 

2

 

Simplify!

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Simplify the expression

 

3

 

 

 

 

 

 

2

6 and 5 do not

divide evenly

7 and 4 do not

divide evenly

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