Negative square roots

[Knownpurpose:1]

Good morning, hope everything is going well,
Is it true that All square roots can only result in positive numbers,, and that a square root will never produce a negative number as its result.?
Thanks in advance for your time and input

 

[Dr.Peterson]

Every positive number has two square roots, one positive and one negative.

The thing that can't be negative is the principal square root, represented by the square root function, [MATH]\sqrt{x}[/MATH]. That's just a matter of definition: We define it that way so that it will be a function, and so that that function has useful properties. There is nothing inherent in the concept of roots that makes any root positive.

 

[pka]

All square roots can only result in positive numbers,, and that a square root will never produce a negative number as its result.?

Please, please read and inwardly digest Prof. Peterson's reply. I have had middle-school mathematics specialist argue with me on this point.
I would say that the square roots of \(4\) are \(\pm 2\) but it incorrect to write \(\sqrt 4=\pm 2\). It on that last bit that people will argue. They want to say but you said "the square roots of \(4\) are \(\pm 2\)". Yes but did you note the 's' on roots? \(\sqrt 4= 2~\&~-\sqrt 4=- 2\). In the real numbers, if \(x\ge 0\) then \(\sqrt x\) in one number, one non-negative real number.

 

[Knownpurpose:1]

Every positive number has two square roots, one positive and one negative.

The thing that can't be negative is the principal square root, represented by the square root function, [MATH]\sqrt{x}[/MATH]. That's just a matter of definition: We define it that way so that it will be a function, and so that that function has useful properties. There is nothing inherent in the concept of roots that makes any root positive.

Thank you very much for your time and assistance!

 

[Knownpurpose:1]

Please, please read and inwardly digest Prof. Peterson's reply. I have had middle-school mathematics specialist argue with me on this point.
I would say that the square roots of \(4\) are \(\pm 2\) but it incorrect to write \(\sqrt 4=\pm 2\). It on that last bit that people will argue. They want to say but you said "the square roots of \(4\) are \(\pm 2\)". Yes but did you note the 's' on roots? \(\sqrt 4= 2~\&~-\sqrt 4=- 2\). In the real numbers, if \(x\ge 0\) then \(\sqrt x\) in one number, one non-negative real number.

Thank you very much that was really helpful!