Find the smallest natural number by which 2401 must be "MULTIPLIED" so that the product is a perfect cube.
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Given : smallest natural number by which 2401 must be "MULTIPLIED" so that the product is a perfect cube
To Find : smallest natural number
Solution:
2401 = 7 * 343
2401 = 7 * 7 * 49
2401 = 7 * 7 * 7 * 7
2401 =7³ * 7
to get perfect cube its must be multiplied by 7² = 49
7³ * 7 * 7²
= ( 7 * 7)³
= 49³
2401 must be "MULTIPLIED" with 49 so that the product is a perfect cube
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