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Find whether each of the following numbers is a perfect square or not (iv) 49

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

(iv) 49

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

So we try to express 49 in successive odd natural numbers. This can also be done by subtracting successive odd natural numbers from 49.

49 - 1 = 48

48 - 3 = 45

45 - 5 = 40

40 - 7 = 33

33 - 9 = 24

24 - 11 = 13

13 - 13 = 0.

Hence 49 is a perfect square number.

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