NCERT Book Class 8 Maths Chapter 5 Squares and Square Roots

SQUARES AND SQUARE ROOTS 51

CHAPTER
Squares and Square
Roots
5
5.1 Introduction
You know that the area of a square = side × side (where ‘side’ means ‘the length of
a side’). Study the following table.

Side of a square (in cm) Area of the square (in cm2)

1 1 × 1 = 1 = 12
2 2 × 2 = 4 = 22
3 3 × 3 = 9 = 32
5 5 × 5 = 25 = 52
8 8 × 8 = 64 = 82
a a × a = a2

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 product of the number with itself.
Such numbers like 1, 4, 9, 16, 25, ... are known as square 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 = 25 and 62 = 36. If 32 is a square number, it must be the square of
a natural number between 5 and 6. But there is no natural number between 5 and 6.
Therefore 32 is not a square number.
Consider the following numbers and their squares.

Number Square

1 1×1=1
2 2×2=4