Long Answer TypeFind 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
Short Answer TypeDo 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.
(i) 92 - 82 = 81-64 = 17 = 9 + 8
102 - 92 = 100-81 = 19 = 10 + 9
152 - 142 = 225-196 = 29 = 15 + 14
1012 - 1002 = 10201-10000 = 201 = 101 + 100
(ii) If (n+1) and (n-1) are two consecutive even or odd natural numbers, then (n+1) x (n-1) = n2 -1
For example
10 x 12 = (11 - 1) x (11+1) = 112 - 1
11 x 13 = (12 - 1) x (12 + 1) = 122 -1
25 x 27 = (22 -1) x (26 - 1) x (26 + 1) = 262 - 1
Can you find the square of the following numbers using the above pattern?
(i) 66666672 (ii) 666666672
Long Answer TypeWhat 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
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
Short Answer TypeThe 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 = ........................
Switch
