Question

The number 600 is written as the product of
its prime factors as
600 = 2 x 35
(a) Find the smallest positive whole number
by which 600 should be multiplied so
that the product is a perfect cube,
(b) Find the smallest positive whole number
by which 600 should be multiplied
so that
the quotient is a perfect cube,​

Answer 1

Answer:

it should be multiplied by 45 and divided by 75 to become a perfect cube

Step-by-step explanation:

by prime factorization we can say

600= 2 x 2 x 2 x 5 x 5 x 3

for a number to be perfect cube the number should have the prime factor in the group of 3.

the number 600 donot  have the prime factors 3 and 5 in group three.

thus the number can be made into a perfect cube by multiplying by 45 or dividing by 75.