Question

By which smallest number must 5400 be multiplied to make it a perfect cube?​

Answer 1

5400 must be multiplied by 5 to make it a perfect cube

Step-by-step explanation:

Given the number 5400

we have to find the smallest number by which the above number is multiplied to make it a perfect cube

The prime factorization is

5400=2\times 2\times 2\times 3\times 3\times 3\times 5\times 5400=2×2×2×3×3×3×5×5

The above number is perfect cube if the all the prime factors occur in three

Therefore to make the above number a perfect cube we multiplied with prime factors which are not in three i.e "5"

hence, 5400 must be multiplied by 5 to make it a perfect cube