Question

Given that 756k is a perfect cube, find the smallest value of k

Answer 1

Answer:

245

Step-by-step explanation:

To make 5×5×7×k a perfect cube, we are to replace k by the product of one more 5 and two more 7 at least, so that rhs will be 5×5×5×7×7×7 I.e 5^3×7^3, then x^3=(5×7)^3=35^3, hence the minimum value of k is 5×7×7=245.