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

(ii) 55

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 55 in successive integers. This can also be done by subtracting successive odd natural numbers from 55.

 

55 - 1 = 54  ;  54 - 3 = 51  ;  51 - 5 = 46  ;  46 - 7 = 39  ;  39 - 9 = 30  ;  30 - 11 = 19  ;  19 - 13 = 6.

Thus 55 is not a perfect square.

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