# Cube Root

How to solve the cube root of a number: 3 examples and their solutions.

## Example 1

### Example

Cube root [^{3}√ ], is the opposite operation of cube [ ^{3}].

Square Root

### Solution

Change the number inside the radical sign, 27,

to a cube.

Think of a number whose square is 27.

3 is good because 3^{3} = 27.

So ^{3}√27 = ^{3}√3^{3}.

Cancel the cube root and the cube.

Then ^{3}√3^{3} = 3.

Cube root and cube are the opposite operations:

just like square and square root.

So you can cancel the cube root and the cube like this.

So 3 is the answer.

## Example 2

### Example

### Solution

Change the number inside the radical sign, -8, to a cube.

Think of a number whose cube is -8.

-2 is good because (-2)^{3} = -8.

So ^{3}√-8 = ^{3}√(-2)^{3}.

Cancel the cube root and the cube.

Then ^{3}√(-2)^{3} = -2.

So -2 is the answer.

## Example 3

### Example

### Solution

Change the number inside the radical sign, -1000, to a cube.

Think of a number whose cube is -1000.

-10 is good because (-10)^{3} = -1000.

So -^{3}√-1000 = -^{3}√(-10)^{3}.

Cancel the cube root and the cube.

Then -^{3}√(-10)^{3} = -(-10).

-(-10) = 10

So -10 is the answer.