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

(i) 121

 

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 121 in successive integers. This can also be done by subtracting successive odd natural numbers from 121.

Applying the concept :-

121 - 1 = 120

120 - 3 = 117

117 - 5 = 112

112 - 7 = 105

105 - 9 = 96

96 - 11 = 85

85 - 13 = 72

72 - 15 = 57

57 - 17 = 40

40 - 19 = 21

21 - 21 = 0

Thus 121 is a perfect square.

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