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Precisely because of what you are saying, the square root of -36 is not -6. The square root is defined, precisely, as the number which, when squared, gives you back the original number, in this case -36; and that isn't the case if you assume that -6 is the square root.

The square root of a negative number can not be taken if you only accept real numbers as solutions. If you accept complex numbers as solutions - and rest assured that complex numbers do have applications in many areas - then you can take the square root of any real (or complex) number. In this case, the square root of -36 is 6i, where "i" is the so-called "imaginary unit".

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11y ago

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