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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) 252 (ii) 2925 |
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Answer» (i) 252 can be factorised as follows.
252 = 2 x 2 x 3 x 3 x 7 Here, prime factor 7 does not have its pair, If we divide this number by 7, then the number will become a perfect square. Therefore, 252 has to be divided by 7 to obtain a perfect square. 252 ÷7 = 36 is a perfect square. 36 = 2 x 2 x 3 x 3 ∴ √36 = 2 x 3 = 6 (ii) 2925 can be factorised as follows.
2925 = 3 x 3 x 5 x 5 x 13 Here, prime factor 13 does not have its pair. If we divide this number by 13, then the number will become a perfect square. Therefore, 2925 has to be divided by 13 to obtain a perfect square. 2925 ÷13 = 225 is a perfect square. 225 = 3 x 3 x 5 x 5 ∴ √225 = 3 x 5 = 15 |
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