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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Simplifying Cube Roots That Contain Integers

To simplify a cube-root radical, we look for perfect cube factors of the radicand.

Example 1

Simplify:

 Solution Write the prime factorization of 250. Group triples of like factors to form perfect cubes. Write as a product of two radicals. Simplify

Thus, in simplified form,

Note:

If you realize that 125 is the largest perfect cube factor of 250, then you can write:

Example 2

Simplify:

Solution

 To simplify this expression, weâ€™ll use the Division Property of Cube Roots to rewrite the radical as a quotient of radicals. Then weâ€™ll simplify each of those radicals. Write the numerator and denominator under separate radical symbols. Write -40 using a perfect cube factor, -8. Write the numerator as the product of two radicals. Simplify the cube roots of any perfect cubes.

Thus, in simplified form,

Note:

If you have difficulty seeing the largest perfect cube that is a factor of -40 or 27, write their prime factorizations.