# Square root

1. Dec 30, 2016

### brycenrg

1. The problem statement, all variables and given/known data
2-squareroot(16) = -2

2. Relevant equations

3. The attempt at a solution
Why is there not two answers? I thought the squareroot of something always has two answers.

2. Dec 30, 2016

### ShayanJ

The square root is supposed to be a function, and a function is not allowed to give more than one output for a given input. So the convention is that $\sqrt{b^2}=+b$. That's the reason every time you solve a quadratic equation, you need to use $\pm$, because you need both positive and negative roots but the square root only gives the positive one.

3. Dec 30, 2016

### PeroK

The equation

$x^2 = 4$

has two solutions.

$x = \pm \sqrt{4} = \pm 2$

The square root of $4$, denoted by $\sqrt{4}$ is the positive solution and is equal to $2$.

It is not the case that $\sqrt{4}=\pm2$.

4. Dec 30, 2016

### ehild

$\sqrt{b^2}=+b$
Correctly: $\sqrt{b^2}=|b|$

5. Dec 30, 2016

### Kaura

Yeah there is the caveat when dealing with square roots in terms of functions that the absolute value or positive root is accepted as the output of the function
However you are correct that square roots typically have two solutions
I suppose it depends on the question or situation

6. Dec 30, 2016

### Ray Vickson

You need to distinguish between two related concepts: (1) the concept of a square root as a solution or solutions of an equation; and (2) the concept of the square root as a mathematical function. When you ask for a square root of 4, there are two possible values, +2 and -2. If you ask for the square root of 4 there is only one value, +2. In any programming language I know of, or in any spreadsheet or on any scientific calculator, when you enter "sqrt" or equivalent, you always get a the single value $\sqrt{b^2} = |b|$.