Comments on: sqrt(16) – how many answers?

By: Murray

Murray — Thu, 18 Nov 2010 06:42:43 +0000

Hi Tammy. Yes, most of the time the square root sign is taken to mean the "principal" square root (that is, the positive case only). And that's my point. In a follow-up post I give the Oxford Concise Dictionary of Mathematics definition of square root.

By: Tammy

Tammy — Wed, 17 Nov 2010 18:01:21 +0000

http://www.mathsisfun.com/algebra/square-root.html

If you scroll about halfway down to the section labeled Principal Square Root, there is an easy-to-understand (to me, anyway) explanation about the fact that a number has both a negative and a positive square root, but the positive one is the Principal Square Root. There is even a graph of an equation showing why this must be the case.

Thoughts?

By: Khurram

Khurram — Tue, 01 Dec 2009 15:25:26 +0000

there is a difference between x^2 = 16 and x = √16
as when we add a root in a question by ourselves than and than only will the answer be ± .If it is given already in the question that x equals to the root of something than the answer will only be the positive one

By: Nabin K. Neupane

Nabin K. Neupane — Sun, 09 Aug 2009 14:45:10 +0000

Thanks for the answer. I agree with u

By: Murray

Murray — Sat, 18 Jul 2009 11:48:26 +0000

Thanks John for your input – and great to hear from you!

By: John

John — Fri, 17 Jul 2009 17:28:07 +0000

Murray is correct. √16 = 4 , not ±4. If the latter were true, then the quadratic formula would not need a ± symbol in it.

Furthermore, the definition of the absolute value function is

|x|=√(x^2)

This would not work were √(x^2)=±x

By: favor

favor — Fri, 26 Jun 2009 21:25:18 +0000

yes, that’s true.
the first equation has two solutions ±√16 which are +4 and -4, but in the second one, the solution is already limited to just one of the two which is +√16 = +4. Period

By: Qlumbo

Qlumbo — Wed, 01 Apr 2009 19:11:46 +0000

Ah. Thanks for the answer. Good point.

By: Murray

Murray — Fri, 06 Mar 2009 01:01:50 +0000

In my post, I did not use the words "square root". I used the radical symbol, √. I agree with the Wikipedia author who wrote:

Every positive number x has two square roots. One of them is √x, which is positive, and the other −√x, which is negative.

This is a notation issue, as well as a semantic one.

By: Qlumbo

Qlumbo — Thu, 05 Mar 2009 22:39:22 +0000

Hmm…that’s weird. Getting a solid definition of square root would entirely answer the question though.

We should also remember that square root is not some super-special operation…you’re just taking the exponent of 0.5.

I’m starting to wonder about the cube root of 8. Cube rooting isn’t special either and belongs in the same group with any other exponent, but just since it isn’t divisible by 2 we come out with one answer without argument.

Definition of square root:
A number that when multiplied by itself equals a given
number.
-4, when multiplied by itself gives 16 and so does 4. And once again, there is nothing wrong with having 2 answers.
Is there anything against this?