Tutoring high school math, cube roots come up a few times a year. The math tutor opens the discussion on simplifying them.

By way of introduction, you might want to read my short article here on perfect cubes and cube roots.

Of course, ³√(8)=2 because (2)(2)(2)=2^3=8. Note that 2^3 is said as “two cubed”.

What about ³√(40)? There is no whole number x such that x^3=40. Yet, ³√(40) can be simplified.

Step 1: Find the factor of 40 that you can take the cube root of (8 in this case).

Step 2: Rewrite ³√(40) as ³√(8)^√3(5).

Step 3: Replace ³√(8)with 2.

We arrive at

³√(40)=³√(8)³√(5)=2(³√(5))

The trick becomes identifying which perfect cube can be factored from the number.

Example: Simplify ³√(192)

Solution:

In this case, realize that 192=(64)(3). Therefore,

³√(192)=³√(64)³√(3)

³√(64)=4. Therefore,

³√(192)=³√(64)³√(3)=4(³√(3))

How we discover 64 as the number to use, and more, will be explored in a post coming soon:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.