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For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square number. Also find the square root of the square number so obtained.(i) 396 (ii) 2645 |
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Answer» (i) 396 can be factorised as follows.
396 = 2 x 2 x 3 x 3 x 11 Here, prime factor 11 does not have its pair. If we divide this number by 11, then the number will become a perfect square. Therefore, 396 has to be divided by 11 to obtain a perfect square. 396 ÷11 = 36 is a perfect square. 36 = 2 x 2 x 3 x 3 ∴ √36 = 2 x 3 = 6 (ii) 2645 can be factorised as follows.
2645 = 5 x 23 x 23 Here, prime factor 5 does not have its pair. If we divide this number by 5, then the number will become a perfect square. Therefore, 2645 has to be divided by 5 to obtain a perfect square. 2645 ÷5 = 529 is a perfect square 529 = 23 x 23 ∴ √529 = 23 |
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