Making a Negative Number Possible to Square RootWe are able to solve x2+4=0 by square rooting both sides, but if we have x2=−4 we can't solve. Firstly, why? Aren't they equal expressions?Secondly, if we have x2=−4, why can't we bring the four to the other side, square root it and then bring it back?

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Making a Negative Number Possible to Square RootWe are able to solve x2+4=0 by square rooting both sides, but if we have x2=−4 we can&#039;t solve. Firstly, why? Aren&#039;t they equal expressions?Secondly, if we have x2=−4, why can&#039;t we bring the four to the other side, square root it and then bring it back?

Nathanial Carey · Accepted Answer

Actually there are a few assumptions we need to explicit. First of all we need to explicit where we are searching the solution for our equation. We can search for natural, integer, rational, real, complex solutions. In this case your question involves the real case.Let&#039;s analize the real case. We can easily see that the problem has no solution because x2≥0 and so x2+4≥4. We can take the square root of both sides of the equation x2+4=0. Before taking the square root we must assume that each side is nonnegative. This is true. Now we have the equation x2+4=0. Again this equation has no solution. If you consider the equation x2=−4, you cannot take the square root of both sides, because one of them is nonnegative. Doing this you are going outside the real numbers and this bring us to the next case. When you are taking a square root in the real numbers you are always assuming that what will be under the root is nonnegative

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