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

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: zac

zac — 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: zac

zac — 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?

By: johnson ojofu

johnson ojofu — Mon, 23 Feb 2009 21:13:41 +0000

hi
as for me i strongly believe that the answer is four, because when u take the square to the other side, it then becomes square sixteen. therefore the square root of sixteen is four

By: zac

zac — Fri, 14 Nov 2008 23:59:24 +0000

Thanks for your opinion, Qlumbo. I am not sure what happens if you are programming and you use the sqrt() function... You get one positive answer, as it should be. I am not sure what happens with maybe other calculators... All calculators give you one positive answer, as they should. There's another example where it is assumed (correctly) that the square root symbol, √, gives a positive answer only. The quadratic equation, which everyone manages to learn sometime in their math career, says: The solution for ax² + bx + c = 0 is x = [-b ± √(b² - 4ac)]/2a If the √ sign meant plus and minus, why then why would we need the ± sign in the formula? √16 is 4, only.