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15 is not a PERFECT square.

So 32 = 9 < 15 < 16 = 42

That is, 15 lies between the squares of 3 and 4. Therefore, there is no integer such that its square is 15.

[Technically, you would also need to prove it for the interval (-4, -3)]

However, 15 is the square of the Irrational Numbers ±sqrt(15) = ±3.873, approx.

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12y ago

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