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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) 2800 (ii) 1620 |
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Answer» (i) 2800 can be factorised as follows.
2800 = 2 x 2 x 2 x 2 x 5 x 5 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, 2800 has to be divided by 7 to obtain a perfect square. 2800 ÷7 = 400 is a perfect square 400 = 2 x 2 x 2 x2 x 5 x 5 ∴ √ 400 = 2 x 2 x 5 = 20 (ii) 1620 can be factorised as follows.
1620 = 2 x 2 x 3 x 3 x 3 x 3 x 5 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, 1620 has to be divided by 5 to obtain a perfect square. 1620 ÷5 = 324 is a perfect square. 324 = 2 x 2 x 3 x 3 x 3 x 3 ∴ √324 = 2 x 3 x 3 = 18 |
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