GED Mathematical Reasoning: Powers And Roots II – Cube Roots

  • The cube root symbol looks a lot like the square root symbol, except that there’s a small “3” sitting in the upper left hand corner. You might relate this to how we say a number is “cubed” when we raise it to a power of three.
  • To cube root a number is the opposite of cubing the number.
  • Here is a listing of “perfect cubes,” which are numbers whose cube root is a whole number.


  • When it comes to SQUARE roots, there is no real number answer for the square root of a negative number. This is because it’s impossible to square a real number and end up with a negative value – since a negative times a negative yields a positive. It’s a different story, though, when we’re dealing with cubed roots.


Example 1

Find the value of: \sqrt[3]{8}


To find the “cube root” of 8, we ask ourselves: What number cubed is equal to 8?

\sqrt[3]{8} = What number cubed is equal to 8

The answer is 2, since 2 times 2 times 2 equals 8. So the cube root of 8 equals 2.

\sqrt[3]{8} = 2


Example 2

Find the value of: \sqrt[3]{-64}


What number cubed is equal to -64?

\sqrt[3]{-64} = What number cubed is equal to -64?

Looking at the listing of perfect cubes, we see that 4 cubed is equal to positive 64. So we might suspect that negative 4 cubed is equal to negative 64. Let’s double check to see if our suspicions are correct.

-4 times -4 is equal to positive 16. And positive 16 times -4 is equal to -64.

math 171

{(-4)}^3 = -64

So the answer is -4. The cube root of -64 is equal to -4.

You have seen 1 out of 15 free pages this month.
Get unlimited access, over 1000 practice questions for just $29.99. Enroll Now