Question

k is a non-zero whole number. Given that 15 x 375 x k is a perfect cube, write down the smallest value of k.​

Answer 1

k = 75
Hope this helps!

Answer 2

k = 75

Explanation:

Let's write down the prime factors of 15 and 375

15 = 3 x 5

375 = 3 x 5 x 5 x 5

So 15 x 375 = 3 x 5 x 3 x 5 x 5 x 5

= (3 x 3) x (5 x 5 x 5) x 5

This cannot be a perfect cube

However if we multiply this by 3 x 5 x 5 we will get

(3 x 3 x ) x (5 x 5 x 5) x(5 x 5 x 5) which is a perfect cube

Since we are asked to find k such that 15 x 375 x k is a perfect cube

k = 3 x 5 x 5 = 75

ans
k = 75