Square Root of 100Date: 04/15/99 at 12:18:12 From: Cody Cry Subject: Why can't -10 be a solution to 100 square rooted? When you take the square root of 100 you get 10. Why can't -10 be an answer? If you square -10 you get 100 also, so why can't 10 and -10 be the answers? Thanks, Cody Cry Date: 04/15/99 at 14:36:53 From: Doctor Rick Subject: Re: Why can't -10 be a solution to 100 square rooted? Hi, Cody! You've asked a good question. What's going on here, I think, is that we have two separate concepts that can easily be confused. One concept is the process of finding the root of a square; for instance, the number x such that x^2 = 100. You know that this has two solutions: 10 and -10 are both roots of this equation. The other concept is the square root FUNCTION. A function takes in one number and returns another number. The number that it returns must be UNIQUE since a function is by definition single-valued. You can't put in 100 and get out both 10 and -10. The square root function is therefore DEFINED so that sqrt(y) returns the NON-NEGATIVE root of x^2 = y. Then we say that the two roots of x^2 = 100 are +-sqrt(100) - that is, plus or minus the [non-negative] square root of 100. Admittedly this is a rather arbitrary definition. But if functions were not single-valued, we'd have a mess. And when you use the square root function in real situations, it will make sense. For instance, the distance between the points (0, 0) and (x, y) is sqrt(x^2 + y^2), and it makes sense that the distance is a non-negative number. The answer I just gave is already in our Dr. Math Archives. Here is something else from our Archives that might add a bit to my reasoning. http://mathforum.org/dr.math/problems/ken.8.28.96.html - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ |
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