Another simple square root problem

[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 don't quite get it. thanks.

 

[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|

 

[dnt]

so its basically a matter of function vs equation?

 

[quantumdude]

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

x=5[/itex] or x=-5<br /> <br /> When you solve the equation by taking the square root (I should say <b>roots</b>), you have to <i>remember</i> that there are two of them.

 

[Fermat]

More or less, yes.

 

[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}.