Simplifying Fractions with RadicalsDate: 03/09/2006 at 21:38:19 From: Sandy Subject: simplifying square roots How do I simplify 18 sqrt 200 divided by 12 sqrt 500? Date: 03/09/2006 at 23:20:06 From: Doctor Ian Subject: Re: simplifying square roots Hi Sandy, Do you mean ____ 18 \/ 200 --------- ? ____ 12 \/ 500 Let's start by noting that because of the way we multiply fractions, we can write this as ____ 18 \/ 200 -- * -------- ____ 12 \/ 500 Do you see why? So if we can simplify each of these fractions separately, we'll be in good shape. Okay? For the first one, we want to find the prime factors of the numerator and denominator: 18 2 * 3 * 3 -- = --------- 12 2 * 2 * 3 How does this help us? Again, breaking things into products of fractions (do you see how we just keep using the same tricks over and over again?), we get 18 2 * 3 * 3 -- = --------- 12 2 * 2 * 3 2 3 3 = - * - * - 2 2 3 3 = 1 * - * 1 2 3 = - 2 So that's how we can simplify the first part. Does that make sense? So, what about that second part? Well, we'll do basically the same thing, but inside the radicals: ____ __________________ \/ 200 \/ 2 * 2 * 2 * 5 * 5 -------- = -------------------- ____ __________________ \/ 500 \/ 2 * 2 * 5 * 5 * 5 How does this help? Well, an important thing to know about square roots is that ______ __ __ \/ a * b = \/ a * \/ b So we can use our little trick again, to get __________________ \/ 2 * 2 * 2 * 5 * 5 = ---------------------- __________________ \/ 2 * 2 * 5 * 5 * 5 __ __ __ __ __ \/ 2 \/ 2 \/ 2 \/ 5 \/ 5 = ---- * ---- * ---- * ---- * ----- __ __ __ __ __ \/ 2 \/ 2 \/ 5 \/ 5 \/ 5 __ \/ 2 = 1 * 1 * ---- * 1 * 1 __ \/ 5 __ \/ 2 = ---- __ \/ 5 Put it together, and we get ____ __ 18 \/ 200 3 \/ 2 -- * -------- = - * ---- ____ 2 __ 12 \/ 500 \/ 5 __ 3 \/ 2 = ------ __ 2 \/ 5 Were you able to follow all that? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ Date: 03/10/2006 at 03:34:41 From: Sandy Subject: Thank you (simplifying square roots) Thank you sooo sooo soooooo much! You have made my day and now I get how to do all my questions. Keep up the good work! |
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