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 33 = 27.
So 327 = 333.

Cancel the cube root and the cube.
Then 333 = 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.