Question

*find the smallest number by which 140625 must be divided, so that the quotient thus obtained is a perfect cube. also find the cube root of the number thus obtained.*​

Answer 1

Given :  Number 140625

To Find :  smallest number by which number is divided so that the quotient thus obtained is a perfect cube.

cube root of the number thus obtained.*​

Solution:

140625  = 3 * 46875

=> 140625  = 3 * 3 * 15625

=> 140625  = 3 * 3 * 5 * 3125

=> 140625  = 3 * 3 * 5 * 5 * 625

=> 140625  = 3 * 3 * 5 * 5 * 5 * 125

=> 140625  = 3 * 3 * 5 * 5 * 5 * 5 * 25

=> 140625  = 3 * 3 * 5 * 5 * 5 * 5 * 5 * 5

=>140625  = 3 * 3 * 5³ * 5³

=>140625  = 9 * 5³ * 5³

140625 must be divided by 9 to obtain a perfect  cube

perfect  cube = 5³ * 5³

=> perfect  cube = 25³

cube root of the number thus obtained.  = 25

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