Algebra Basics

- Number Line and Signed Numbers I - Adding
- Number Line And Signed Numbers II - Subtracting
- Number Line And Signed Numbers III - Multiplying & Dividing
- Powers And Roots I
- Powers And Roots II - Cube Roots
- Scientific Notation
- Order Of Operations
- Absolute Value
- Algebra Basics Quiz I
- Algebra Basics Quiz II
- Algebra Basics Quiz III
- Algebra Basics Quiz IV

# 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:

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

**Example 2**

Find the value of:

What number cubed is equal to -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.

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