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 5^{2} = 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 3^{3} = 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