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For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained.(i) 1458 (ii) 768 |
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Answer» (i) 1458 can be factorised as follows.
1458 = 2 × 3 × 3 × 3 × 3 × 3 × 3 Here, prime factor 2 does not have its pair. If 2 gets a pair, then the number will become a perfect square. Therefore, 1458 has to be multiplied with 2 to obtain a perfect square. Therefore, 1458 × 2 = 2916 is a perfect square. 1458 × 2 = 2916 = 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3 ∴ √2916 = 2 x 3 x 3 x 3 = 54 (ii) 768 can be factorised as follows.
768 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 Here, prime factor 3 does not have its pair. If 3 gets a pair, then the number will become a perfect square. Therefore, 768 has to be multiplied with 3 to obtain a perfect square. Therefore, 768 × 3 = 2304 is a perfect square. 768 × 3 = 2304 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 ∴ √2304 = 2 x 2 x 2 x 2 x 3 = 48 |
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