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I have a question that came into my mind while solving some problems. If I have a constant times an expression in a square root like ##4\sqrt{16}## I can square the constant and push it into the square root: ##4\sqrt{16}=\sqrt{4^2 16} = 16##. But what if the constant outside of the square root is negative? Then I will get a contradiction: ##-4\sqrt{16} = \sqrt{(-4)^2 16} = \sqrt{4^2 16} = 16 ≠ -16##. Why is this happening? Clearly I cannot square negative numbers the same way as I do with positive ones, but why?

Any comments will be appreciated!