How can the square root of a number be a well defined function when there are two possible answers.?

Question

I thought functions could only have one answer. Or is square root not a function.

Answer 1

There are NOT two values!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

The square root of 25 is 5 and that is it.

When you solve x^2=25 then you get two different answers for x: x is 5 or x is -5. What people fail to realize is that "solving x^2=25" and "evaluating square root of 25" are two different problems.

(Different problems with a close connection...but different problems nonetheless!)

Answer 2

A square root of a number can be a well defined function even if the problem has two answers.
As you should have learned in school a square root can have two answers. One of the answers is positive and the other answer is negative.
There is one exception though. It only occurs when there is an i. i means that it is a negative square root.
the answer to a square root problem is usually written as plus or minus the number as in the square root of 25. the answer is plus or minus five.
this is the answer because positive five squared is 25 and negative five squared is 25 (positive because the negatives canceled each other out)

Answer 3

Because when we speak of the square root and express it, we usually refer to the "principle" or "positive" square root.

y = sqrt(x)

is a function that is half of a sideways parabola, and this is because we're only taking the positive square root.

In the case of

y^2 = x,

THEN we would have to answers, y = +/- sqrt(x), and this wouldn't be a function.

Thus, it depends on the context of how you're using square root. The button on your calculator won't give you two answers simply because it's the version of the square root that works as a function.

That's why sqrt(4) = 2, whereas, if
x^2 = 4, then
x = +/- 2 {adding the plus or minus is part of the algebra involved in taking the square root of both sides}

Answer 4

there are different type of functions and it is not neccessary that a function has one value
if you have
f(x)=sqrtx
then you take the the +ve sqrt values of x as is indicated by the function but if u have
x^2=4
then x=+/-2

Answer 5

There can be more than
one answers. Consider number 4
Sqrt of 4 is+-2. This is because:
2*2=4
-2*-2=4
A quadratic equation will have two roots.
A cubic will have three roots.Similarly
a polynomial of nth degree will have n roots.

Answer 6

3i (square root sign) 3

Answer 7

They usually want the absolute value of the possible return values, or in the case where there can be an imaginary part of the return, they also usually want the real part of the return.