Posted by **Dorothy** on Tuesday, May 22, 2012 at 4:22pm.

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

- Math -
**MathMate**, Tuesday, May 22, 2012 at 9:51pm
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.

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