Year 7 Interactive Maths - Second Edition

Patterns

Square Numbers

A square number is a number that can be arranged in a square pattern. The patterns of the first three square numbers are depicted below.

So, there is 1 × 1 = 1 dot in this square number.

So, there are 2 × 2 = 4 dots in this square number.

So, there are 3 × 3 = 9 dots in this square number.

Following the pattern above, we can find any particular square number.

E.g.  The fourth square number will form a square with 4 rows each containing 4 dots.
So, there are 4 × 4 = 16 dots in the square.

Likewise, the fifth square number will form a square with 5 rows each containing 5 dots.
So, there are 5 × 5 = 25 dots in the square.

Note that 5² is often read as '5 to the power 2' and 2 is called the index (or power).

Index Form

If a number is written with an index, then it is said to be in index form.

E.g.  36 can be written as 6² .

Example 1

Write the tenth square number.

Solution:

The tenth square number will form a square with 10 rows each containing 10 dots.

Example 2

Write down a number between 50 and 100 that is both odd and square.

Solution:

We find that 81 is between 50 and 100, and it is both an odd and square number.
So, the required number is 81.

Example 3

Write 20 × 20 in index form.

Solution:

Example 4

Write 12² in words.

Solution:

12² in words is 'twelve squared'.

Key Terms

patterns, square numbers, index form