# Squares, Cubes and Roots

## Squares

To square a number we multiply the number by itself.
3 squared is 9 because 3 × 3 = 9
4 squared is 16 because 4 × 4 = 16

We can write squared using a small (superscript) 2.
5² means 5 squared
10² means 10 squared

Example 1:
Work out the value of 9²

To work out the value of 9 squared we need to calculate 9 × 9
9 × 9 = 81
9² = 81

Example 2:
Work out the value of (-8)²

To work out the value of -8 squared we need to calculate -8 × -8
-8 × -8 = 64 (A negative times a negative is a positive)
(-8)² = 64
If you are using a calculator you must put the -8 in brackets, otherwise the calculator will get the answer wrong!

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## Cubes

To cube a number we multiply the number by itself, and then multiply that answer by the number again.

We can write cubed using a small (superscript) 3.
2³ means 2 cubed
3³ means 3 cubed

Example 3:
Work out the value of 4³

To work out the value of 4 cubed we need to calculate 4 × 4 × 4
4 × 4 = 16
16 × 4 = 64
4³ = 64

Example 4:
Work out the value of 10³

To work out the value of 10 cubed we need to calculate 10 × 10 × 10
10 × 10 = 100
100 × 10 = 1000
10³ = 1000

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## Square Roots

Square rooting is the opposite of sqauring a number.
9² = 81, so the square root of 81 is 9

Square root 100 can be written as √100
√81 means square root 81

Example 5:
Work out the value of √144

We are looking for the number that multiplies by itself to make 144
12 × 12 = 144
√144 = 12

Example 6:
Work out the value of √100

We are looking for the number that multiplies by itself to make 100
10 × 10 = 100
√100 = 10

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## Cube Roots

Cube rooting is the opposite of cubing a number.
10³ = 1000, so the square root of 1000 is 10

Cube root 125 can be written as ∛125
∛216 means cube root 216

Example 7:
Work out the value of ∛8

We are looking for the number that multiplies by itself, and then by itself again, to make 8
2 × 2 × 2 = 8
∛8 = 2

Try this: