Why Can't the Square Root of a Negative Number Be a Real Number?Date: 12/07/2003 at 14:56:08 From: Stephanie Subject: square roots Can you explain why you can't find the square root of a negative number on the real number line? Date: 12/07/2003 at 19:28:07 From: Doctor Schwa Subject: Re: square roots Hi Stephanie, The square root of a number is something that, multiplied by itself, gives the number you're taking the square root of. Suppose the square root is positive. Then, if you multiply it by itself, you will get a positive result since a positive times a positive makes a positive. So, the number you're taking the square root of must be positive. How about if the square root is negative? Then, if you multiply it by itself, the number you're taking the square root of still must be positive, because a negative times a negative is also a positive. How about if the square root is zero? Then the number you're taking the square root of is zero since 0 * 0 = 0. That covers the whole number line, so any square root you can find on the real number line must be the square root of a positive number or zero. It's impossible for it to be the square root of a negative number. This is why in the context of real numbers we say that you cannot take the square root of a negative number. There is no real number that you can square and get a negative result. Does that help? - Doctor Schwa, The Math Forum http://mathforum.org/dr.math/ |
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