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Question -

How many numbers lie between squares of the following numbers?
(i) 12 and 13
(ii) 25 and 26
(iii) 99 and 100.



Answer -

(i)We know that numbers between n2 and (n + 1)2 = 2n
Numbers between 12
2 and 132 = (2n) = 2 × 12 =24
(ii) Numbers between 25
2 and 262 = 2 × 25 = 50 ( n = 25)
(iii) Numbers between 99
2 and 1002 = 2 × 99 = 198 ( n = 99)

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