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90 MATHEMATICS

3 3 × 3 = 9
4 4 × 4 = 16 Can you
5 5 × 5 = 25 complete it?
6 -----------
7 -----------
8 -----------
9 -----------
10 -----------

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 square numbers. These numbers are also called perfect
squares.

TRY THESE

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

6.2 Properties of Square Numbers
Following table shows the squares of numbers from 1 to 20.

Number Square Number Square

1 1 11 121
2 4 12 144
3 9 13 169
4 16 14 196
5 25 15 225
6 36 16 256
7 49 17 289
8 64 18 324
9 81 19 361
10 100 20 400

Study the square numbers in the above table. What are the ending digits (that is, digits in
the one’s place) of the square numbers? All these numbers end with 0, 1, 4, 5, 6 or 9 at
unit’s place. None of these end with 2, 3, 7 or 8 at unit’s place.
Can we say that if a number ends in 0, 1, 4, 5, 6 or 9, then it must be a square
number? Think about it.

TRY THESE

1. Can we say whether the following numbers are perfect squares? How do we know?
(i) 1057 (ii) 23453 (iii) 7928 (iv) 222222
(v) 1069 (vi) 2061