Simplifying Cube Roots That Contain Integers
To simplify a cuberoot 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.
