Principal Square Root PositiveDate: 10/24/2002 at 14:40:31 From: Arthur Subject: Principal Square Roots I was just wondering why it's always taught that the principal square root of a number is positive. Is there any reason, (except that a function must get only one value of f(x) for every value of x) that the second, negative square root is rejected? If so, why not reject the positive root, accepting the negative root to be the principal one? Arthur Date: 10/24/2002 at 17:09:55 From: Doctor Peterson Subject: Re: Principal Square Roots Hi, Arthur. Probably the main reason we choose the positive root is that positive numbers are more familiar and useful. If we use the Pythagorean theorem to find the length of a hypotenuse, we expect to get a positive number. In addition, if the principal root were negative, we could not say sqrt(a) * sqrt(b) = sqrt(ab) because, for example, sqrt(4) * sqrt(9) = -2 * -3 = 6 while sqrt(4*9) = sqrt(36) = -6 So it's a lot easier to take it the way we do. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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