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# Square and Cube Numbers

Square and cube numbers are formed by multiplying a number by itself. When a number is multiplied by itself, we get a square of that number, and when a number is multiplied by itself thrice, we get its cube number.

Let’s look at square and cube numbers in greater detail:

## Square numbers and Square roots

Square numbers are formed when we multiply a number by itself. For example, 5 x 5 = 25.

A square number is represented by the power of ‘2’. So 52 = 25. You will read it as “5 to the power of 2” or “5 square”.

The opposite of square is square root, and it is given by the symbol 1. To find the square root of a number, we try and split the number into two same numbers and apply the square root.

For example – = =  15

2. To find the square root of a number using its prime factors, take one factor from each pair of like factors, and multiply them to get the square root. = = =  7 x 2  =  14

## Cube and Cube roots

Cube numbers are formed by multiplying a number by itself thrice.

3 x 3 x 3 = 27. This is represented as 33 = 27, and you will read it as “3 to the power of 3” or “3 cube”. The opposite of cube is cube root, and it is given by the symbol 1. To find the cube root, we find a number which multiplied by itself thrice give the number in the cube root.

So = =  5

2. To find the cube root of a number using its prime factors, take one factor from each three like factors, and multiply them together to obtain the cube root.

For example – = = =  2 x 2 x 2  =  8

3. For larger numbers, you could attempt to split it into two, and work out the cube roots of these two numbers, and multiply them to get the cube root. = x = x =  3 x 10  =  30