Question

Given that 1800k is a perfect cube, write the smallest possible value of k

Answer 1

Answer: 15

Step-by-step explanation:

A perfect cube is a whole number which is the cube of another whole number.

Since, the factor form of 1800 = $2\times 2\times 2\times 3\times 3\times 5\times 5$

=  $2^3\times 3^2\times 5^2$

Thus, we need to multiply 15 in the number 1800 for making it a perfect cube.

When we multiply 1800 by 15,

We get, 27000 which is a perfect square root.

Thus, the smallest value of k will be 15.