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How many non square numbers lie between the following pairs of numbers (i) 100^2 and 101^2  (ii) 90^2 and 91^2  (iii) 1000^2 and 1001^2.

Q.2 How many non square numbers lie between the following pairs of numbers

(i) 100^{2}\; and\; 101^{2}

(ii) 90^{2}\; and\; 91^{2}

(iii) 1000^{2}\; and\; 1001^{2}

Answers (1)
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In general, we can say that there are 2n nonperfect square numbers between the squares of the numbers n and (n + 1). 

(i) The number of non-square numbers that lie between the square of 100 and 101 will be = 2(100)  = 200.

(ii) The number of non-square numbers that lie between the square of 90 and 91 will be = 2(90) = 180.

(iii) The number of non-square numbers that lie between the square of 1000 and 1001 will be = 2(1000) = 2000.

 

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