Question

What is the smallest integer n so that the square root of 3n is a multiple of 4

Answer 1

4k : k∈Z is an integer which is a multiple of 4.

Its square is 16k^2.
For 3n=16k^2, we have n=16k^2/3 ∈Z, so 3 must divide k^2, which in turn means that 3 divides k.
So the smallest n is when k=3, or
n=16*3^2/3=48
assuming n is a positive integer.