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Square Numbers for the 11 Plus Exams

1. What is a square number?

A number multiplied by itself is called a square number. ‘A number squared’ is also called a square number.
² is a symbol used to denote a square number.

Example of square numbers:
3² = 3×3 = 9
4² = 4×4 = 16

1.2  How to work out Square Numbers?

To work out a square number, you have to multiply a number by itself.

For example,  4 x 4 = 16. This can also be shown as 4^2 or 4².

2. List of square numbers

1² = 1 × 1 = 1 11² = 11 × 11 = 121
2² = 2 × 2 = 4 12² = 12 × 12 = 144
3² = 3 × 3 = 9 13² = 13 × 13 = 169
4² = 4 × 4 = 16 14² = 14 × 14 = 196
5² = 5 × 5 = 25 15² = 15 × 15 = 225
6² = 6 × 6 = 36 16² = 16 × 16 = 256
7² = 7 × 7 = 49 17² = 17 × 17 = 289
8² = 8 × 8 = 64 18² = 18 × 18 = 324
9² = 9 × 9 = 81 19² = 19× 19 = 361
10² = 10 × 10 = 100 20² = 20 × 20 = 400

 

2.1 Why are they called square numbers?

The numbers listed in the above table are called square numbers or squared numbers because they gives the area of a square. As you remember, all the sides of the square are equal in length and so the area of the square is simply calculated by multiplying the side by itself.

For example: for square of side 6 cm, area of square is 6 × 6 or 6² which is 36 cm². Also if the area of a square is 25 cm², the side of the square will be 5 cm as 5² = 5 × 5 = 25.

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