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

  • Math -

    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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