Find the smallest number by which 2560 must be multiplied so that the product is a perfect cube - Maths - Cubes and Cube Roots

Question

Find the smallest number by which 2560 must be multiplied so
that the product is a perfect cube

Ajanta Trivedi · Accepted Answer

first we will write 2560 in its prime factors.

$2560 = 2^{9} * 5 = (2^{3})^{3} * 5$

thus the power of $2^{3}$ is 3. to make the number a perfect cube , we need to make the power of 5 also 3.

thus we must multiply be $5^{2} = 25$

so must multiply by 25 to make 2560 a perfect cube.

hope this helps you.

cheers!!

Find the smallest number by which 2560 must be multiplied so that the product is a perfect cube.