Simplifying Cube Roots

Front

What is a cube root?

Back

A cube root of a number is a value that, when multiplied by itself three times, gives the original number. For example, the cube root of 27 is 3, because 3 x 3 x 3 = 27.

Front

How do you simplify cube roots?

Back

To simplify cube roots, factor the number under the radical into its prime factors and group them into sets of three. Each set of three can be taken out of the radical.

Front

What is the cube root of 64?

Back

The cube root of 64 is 4, because 4 x 4 x 4 = 64.

Front

What is the cube root of a product?

Back

The cube root of a product is the product of the cube roots. For example, @@ ext{If } a = 8 ext{ and } b = 27, ext{ then } oot{3}{a imes b} = oot{3}{8} imes oot{3}{27} = 2 imes 3 = 6.$$

Front

What is the cube root of 1,728?

Back

The cube root of 1,728 is 12, because 12 x 12 x 12 = 1,728.

Front

How do you express cube roots in simplest form?

Back

To express cube roots in simplest form, factor the number under the radical and simplify by removing perfect cubes.

Front

What is the relationship between cube roots and exponents?

Back

The cube root of a number can be expressed as an exponent: @@ oot{3}{x} = x^{rac{1}{3}}@@.

Front

What is the cube root of 27?

Back

The cube root of 27 is 3, since 3 x 3 x 3 = 27.

Front

How do you find the cube root of a fraction?

Back

To find the cube root of a fraction, take the cube root of the numerator and the denominator separately. For example, @@ oot{3}{rac{8}{27}} = rac{ oot{3}{8}}{ oot{3}{27}} = rac{2}{3}.$$

Front

What is the cube root of 125?

Back

The cube root of 125 is 5, because 5 x 5 x 5 = 125.