2 Divided by the Square Root of 2Date: 11/10/95 at 7:58:7 From: Braun Tillmann Subject: math Why does 2/sqrt 2=sqrt 2 ? Date: 11/10/95 at 11:10:41 From: Doctor Ken Subject: Re: math Hello there! I think that the easiest way to see this problem is to realize that 2 = Sqrt{2} * Sqrt{2}. So the left part of your equation becomes Sqrt{2} * Sqrt{2} ----------------- Sqrt{2} and you can see that that equals Sqrt{2} by cancellation. Actually, it will work for any number, not just 2 (as long as the number is bigger than zero). Let's say you have a positive number, and let's call it x. Then we can just replace the 2 by an x and everything still works: x Sqrt{x} * Sqrt{x} x = Sqrt{x} * Sqrt{x}. So ------- = ----------------- Sqrt{x} Sqrt{x} , and you can see that that equals Sqrt{x} by cancellation. In fact, if you know about imaginary numbers, then the above proof works for ANY x, as long as it's not zero. -Doctor Ken, The Geometry Forum |
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