IXL - Simplify radical expressions with variables (Precalculus practice)

Simplify the radical expression.

361

Write your answer in the form

where

and

are constants or expressions in

Use at most one radical in your answer, and at most one absolute value symbol in your expression for

ref_doc_title.

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question

Simplify the radical expression.

Write your answer in the form

where

and

are constants or expressions in

Use at most one radical in your answer, and at most one absolute value symbol in your expression for

key idea

For real numbers

and

and a positive integer

is an

root of

For example, 2 is a fourth root of 16 because

In the expression

the symbol

is called the

radical,

is called the

index,

and

is called the

radicand.

the radical is a square root and the 2 is not written:

is even,

In this case, the radical outputs a non-negative value.

is odd,

and

are both

roots, then

solution

To start, identify the type of root in the question.

Since the index is 3, this is a cube root. So, factor the radicand and group the cubes.

Factor the radicand

Make cube terms if you can

(

)

Make cube terms if you can

Group the cubes

(

)

Group the cubes

Since

is odd,

(

)

Since

is odd,

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