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Maths

Powers and roots - Foundation

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In this Revision Bite we are going to look at:

# Squares, cubes and their roots

## Squaring a number

32 means '3 squared', or 3 x 3.

The small 2 is an index number, or power. It tells us how many times we should multiply 3 by itself.

Similarly 72 means '7 squared', or 7 x 7.

And 102 means '10 squared', or 10 x 10.

So, 12 = 1 x 1 = 1

22 = 2 x 2 = 4

32 = 3 x 3 = 9

42 = 4 x 4 = 16

52 = 5 x 5 = 25

etc

1, 4, 9, 16, 25… are known as square numbers.

## Square roots

The opposite of a square number is a square root.

We use the symbol to mean square root.

So we can say that = 2 and = 5.

However, this is not the whole story, because -2 x -2 is also 4, and -5 x -5 is also 25.

So, in fact, = 2 or -2. And = 5 or -5.

Remember that every positive number has two square roots.

## Cubing a number

2 x 2 x 2 means '2 cubed', and is written as 23.

13 = 1 x 1 x 1 = 1

23 = 2 x 2 x 2 = 8

33 = 3 x 3 x 3 = 27

43 = 4 x 4 x 4 = 64

53 = 5 x 5 x 5 = 125

etc

1, 8, 27, 64, 125… are known as cube numbers.

## Cube roots

The opposite of a cube number is a cube root. We use the symbol to mean cube root.

So is 2 and is 3.

Each number only has one cube root.

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