square roots

[jacqueline]

My teacher gave out this question:

Why is the square root of 4 always 2, or -2?

4 isn't a special number, he just chose to use 4. It can be why is the square root of 9 always 3 or -3, etc etc.

 

[stapel]

Why is the square root of 4 always 2, or -2?

In general usage, sqrt[4] is just 2, not ±2. But aside from that, what else would sqrt[4] equal?

I mean, the question is like asking "why is two plus two always four?" What else would it be?

Eliz.

 

[pka]

Why is the square root of 4 always 2, or -2?
I would have an argument with your teacher!
The word ‘the’ in the question is a quantifier: it means one!
He gave you two!

Had he put it as “Why are the square roots of 4 always 2, or -2?” then there would be no difficulty. Even better, “Why are there two square roots of any positive number; one positive and one negative?”

Well if n>0 then x<SUP>2</SUP>=n has two roots: \(\displaystyle \left( { \pm \sqrt n } \right)^2 = n\)