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By repeated subtraction of odd numbers starting from find whether the following numbers are perfect squares or not If the number is a perfect square then find its square root

By repeated subtraction of odd numbers starting from 1, find whether the following numbers are perfect squares or not? If the number is a perfect square then find its square root.

(i) 121

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Consider \sqrt{81}. Then

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.

Since zero is obtained in the 9th step thus \sqrt{81} = 9.

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