what is the least number with which 6075 should be multiplied to make it a perfect cube? also find the cube root of that number.

Question

what is the least number with which 6075 should be multiplied to make it a perfect cube? also find the cube root of that number.

(PLEASE SOLVE IT WITH STATEMENTSISN YOUR COPY)​

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Amara 2 weeks 2021-09-07T02:50:23+00:00 1 Answer 0 views 0

Answers ( )

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    2021-09-07T02:52:18+00:00

    Answer:

    The least number to be multiplied is 15 and the cube root of the new number is 45

    Step-by-step explanation:

    Prime factorization of 6075 is

    6075 = 3⁵ x 5²

    To make this a perfect cube, power of 3 and 5 should be made a multiple of 3. The least number to be multiplied to satisfy this condition is 3×5 or 15 .The new number is

    6075x 15 = 3⁶ x5³.

    Cube root of the new number is

     {( {3}^{6} . {5}^{3} )}^{ \frac{1}{3} }

    or \:  {3}^{ \frac{6}{3} } . {5}^{ \frac{3}{3} }

    or \:  {3}^{2} . {5}^{1}

    or \: 9 \times 5 = 45

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