Question

Find the smallest number which when multiplied with 3600 will make the product perfect cube.Further find the cube root of the product.

Answer 1

We can solve this by prime factorization method:

³√3600x2x2x3x5 = ³√2x2x2x2x2x2x3x3x3x5x5x5

= ³√2³x2³x3³x5³

= ³√(2x2x3x5)³

=³√(60)³

= [(60)³]^⅓

= 60

So ³√216000 = 60.