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)​

Answer 1

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 3x5 or 15 .The new number is

6075x 15 = 3⁶ x5³.

Cube root of the new number is

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

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

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

$or \: 9 \times 5 = 45$