Answer:
[tex]\huge\boxed{ \text{(A)}\ \ \frac{1}{10}, -\frac{1}{10}}[/tex]
Step-by-step explanation:
We can simplify this expression down so that we have x isolated on one side of the equation.
So we can take the square root of both sides.
[tex]x = \sqrt{\frac{1}{100}}[/tex]
The square root of [tex]\frac{1}{100}[/tex] will be the number that, when multiplied by itself, will get us [tex]\frac{1}{100}[/tex].
In order to find the square root of a fraction, the numerator squared must correct and the denominator squared must be correct.
[tex]1^2 = 1[/tex]
[tex]10^2 = 100[/tex]
This means that we have the values 1 and 10. Therefore one of our fractions is [tex]\frac{1}{10}[/tex].
HOWEVER: A negative number squared is a positive. So this also works:
[tex]-1^2 = 1\\\\-10^2=10[/tex]
So we have [tex]-\frac{1}{10}[/tex] along with [tex]\frac{1}{10}[/tex].
Hope this helped!
