Square Roots and FractionsDate: 10/25/98 at 17:57:56 From: Billy Dickson Subject: Dividing Equations How do you simplify a square root with a fraction? I have problems like: ___ / 1 _ / --- \/ 2 Help! Billy Dickson Date: 10/27/98 at 08:49:33 From: Doctor Peterson Subject: Re: Dividing Equations Okay, Billy, presumably what you are supposed to do is to simplify the expression. There's nothing you can do to eliminate the square root (other than actually evaluating it, which would be only an approximation), but we can simplify it so that we only take the square root of an integer (not a fraction), and all square roots are in the numerator (so that when we evaluate it we won't have to divide by a lot of digits). Simplifying radical expressions like this sometimes also requires making the number inside the square root sign as small as possible, but we won't have to do that in this problem. In e-mail, we write the square root as "sqrt", so your problem becomes: Simplify sqrt(1/2) What we do is to first use the rule that: sqrt(a/b) = sqrt(a) / sqrt(b) so we have: sqrt(1) 1 sqrt(1/2) = ------- = ------- sqrt(2) sqrt(2) Now we only have the square root of an integer, but it's in the denominator. How can we move it? If we multiply sqrt(2) by itself, we get an integer, 2; so let's multiply both numerator and denominator by sqrt(2), which won't change the value: 1 1 * sqrt(2) sqrt(2) ------- = ----------------- = ------- sqrt(2) sqrt(2) * sqrt(2) 2 That's the answer. If you want to go on and evaluate it, you don't even need a calculator, if you know that approximately sqrt(2) = 1.414. This tells us that sqrt(1/2) is about 0.707. That would have been much harder to figure out without simplifying first. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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