# Another simple square root problem

1. Dec 15, 2005

### dnt

why is the square root of 25 just 5

but when the question x^2 = 25, the answer becomes +/- 5?

whats the logic here? i dont quite get it. thanks.

2. Dec 15, 2005

### Fermat

Square root is a function that returns the positive value only.

When you have the eqn,

X² = 25

then both x=5 and x = -5 are solutions of the eqn,

Which is why you write down the answer as x = +/- 5

If you applied the square root function to x², you would get

Sqrt(x²) = |x|

3. Dec 15, 2005

### dnt

so its basically a matter of function vs equation?

4. Dec 15, 2005

### Tom Mattson

Staff Emeritus
Solving the equation $x^2=25$ by taking the square root is a bit sloppy, IMO. What you are really doing is a shortcut for the following:

$x^2-25=0$

$(x-5)(x+5)=0$

$x-5=0$ or $x+5=0$

[tex]x=5[/itex] or $x=-5$

When you solve the equation by taking the square root (I should say roots), you have to remember that there are two of them.

5. Dec 15, 2005

### Fermat

More or less, yes.

6. Dec 16, 2005

### HallsofIvy

In general, an equation like x2= a has two solutions.
One is the square root of a: $\sqrt{a}$.
The other is the negative of the square root of a:$-\sqrt{a}$.