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 [itex]x^2=25[/itex] by taking the square root is a bit sloppy, IMO. What you are really doing is a shortcut for the following:

[itex]x^2-25=0[/itex]

[itex](x-5)(x+5)=0[/itex]

[itex]x-5=0[/itex] or [itex]x+5=0[/itex]

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

When you solve the equation by taking the square root (I should say roots), you have to remember 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: [itex]\sqrt{a}[/itex].
The other is the negative of the square root of a:[itex]-\sqrt{a}[/itex].