Find whether each of the following numbers is a perfect square or not?

(i) 121 (ii) 55 (iii) 81

(iv) 49 (v) 69

Express the following as the sum of two consecutive integers.

(i) 21² (ii) 13² (iii) 11² (iv) 19²

Do you think the reverse is also true, i.e. is the sum of any two consecutive positive integers is perfect square of a number? Give example to support your answer.

The difference between the squares of two consecutive natural numbers is equal to the sum of the two numbers.

Write the square, making use of the above pattern.

(i) 111111² (ii) 11111112

Can you find the square of the following numbers using the above pattern?

(i) 6666667² (ii) 66666667²

What will be the unit digit of the squares of the following numbers?

(i) 81 (ii) 272 (iii) 799 (iv) 3853 (v) 1234 (vi) 26387 (vii) 52698 (viii) 99880 (ix) 12796 (x) 55555

18.

The following numbers are obviously not perfect squares. Give reason.

(i) 1057 (ii) 23453 (iii) 7928 (iv) 222222 (v) 64000 (vi) 89722 (vii) 222000 (viii) 505050

The squares of which of the following would be odd numbers?

(i) 431 (ii) 2826 (iii) 7779 (iv) 82004

Observe the following pattern and find the missing digits.

11² = 121
101² = 10210
1001² = 1002001
100001² = 1 ............. 2 ..............1
10000001² = ........................