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### Principal Square Root Positive

```Date: 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/
```
Associated Topics:
High School Definitions
High School Square & Cube Roots
Middle School Definitions
Middle School Square Roots

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