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.
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
Since the square of an odd natural number is odd and that of an even number is an even number.
∴ (i) The square of 431 is an odd number
(∵ 431 is an odd number)
(ii) The square of 2826 is an even nnumber.
(∵ 2826 is an odd number)
(iii) The square of 7779 is an odd number
(∵ 7779 is an odd number)
(iv) The square of 82004 is an even nnumber.
(∵ 82004 is an odd number)
Observe the following pattern and find the missing digits.
112 = 121
1012 = 10210
10012 = 1002001
1000012 = 1 ............. 2 ..............1
100000012 = ........................
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