# Squares and square roots; cubes and cube roots

## Squares and square roots; cubes and cube roots

When a number is multiplied by itself (once), we say that it is **squared**. The index '2' is written in superscript after the number that is being squared.

For example:

7 ´ 7 = 7 squared

= 7^{2}

= 49

The original number is the square root of the result. Finding the square root is the reverse of squaring a number. The square root symbol is .

For example:

5^{2} = 5 ´ 5

= 25

= 5

When a number is multiplied by itself and then by the original number again, we say that it is **cubed**. The index '3' is written in superscript after the number that is being cubed.

For example:

8 ´ 8 ´ 8 = 8 cubed

= 8^{3}

= 512

The original number is called the cube root of the result. Finding the cube root is the reverse of cubing a number. The cube root symbol is

For example:

4^{3} = 4 ´ 4 ´ 4

= 64

therefore = 4