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

(iii) 81

Answers (1)

If it is a sum of successive odd natural numbers starting with 1, then it is a perfect square.

So we try to express 81 in successive odd natural numbers. This can also be done by subtracting successive odd natural numbers from 81.

81 - 1 = 80

80 - 3 = 77

77 - 5 = 72

72 -  7 = 65

65 - 9 = 56

56 - 11 = 45

45 - 13 = 32

32 - 15 = 17

17 - 17 = 0

Thus 81 is a perfect square number.

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