Introduction

Click on instructions button for directions on how to use the component and solve the given problems.

You know that the area of a square = × (where ‘side’ means ‘the length of a side’).

Study the following table

What is special about the numbers 4, 9, 25, 64 and other such numbers?

Since, 4 can be expressed as 2 × 2 = 22, 9 can be expressed as 3 × 3 = 32, all such numbers can be expressed as the of the number with itself.

Such numbers like 1, 4, 9, 16, 25, ... are known as numbers.

In general, if a natural number m can be expressed as n2, where n is also a natural number, then m is a square number.

Is 32 a square number? We know that 52 = and 62 = .

If 32 is a square number, it must be the square of a natural number between 5 and 6. But there is natural number between 5 and 6.

Therefore, 32 a square number.

Thus, the square of ${a} is ${a*a}. (Move the arrows to change the values)

Consider the following numbers and their squares

From the above table, can we enlist the square numbers between 1 and 100? Are there any natural square numbers upto 100 left out?

You will find that the rest of the numbers are not square numbers.

The numbers 1, 4, 9, 16 ... are numbers.

These numbers are also called perfect squares.

Find the perfect square numbers between (i) 30 and 40 (ii) 50 and 60

(i) Between 30 and 40:

The squares of integers around these numbers are: 52 = i.e ( than 30)

62 = ( the range)

72 = ( than 40)

Perfect square in this range: 36.

(ii) Between 50 and 60:

The squares of integers around these numbers are: 72 = i.e ( than 50)

82 = i.e ( than 60)

There are no perfect squares between 50 and 60.

Squares and Square Roots