Cube Roots

3a b

• a is a cube root of b if and only if

• Example 1

2 is a cube root of 8, since 32 8

- 2 is a cube root of - 8, since 32 8

• Note a key difference between square roots and cube roots:

Square Root

23 9

23 9

The number 9 has two square roots, -3 and 3.

Cube Root

The number 8 has one cube root, 2.

32 8

• Recall that when using radical notation, the square root is equal to the principal (nonnegative) square root.

3 3a a

• Also, when simplifying a square root, it was sometimes necessary to use an absolute value sign.

• The cube root is much simpler, and is defined as:

2a a

• Example 2

Evaluation Reasoning

3 64 4 34 64

3 8 2 32 8

• Example 3

2x

Simplify

33 2x

33 2x

• Example 4

Simplify 3 327x

First write the radicand as a quantity cubed.

3 327x 3 33 3 x

33 3x

3x