I have the following:
$\displaystyle {(4 - \frac{1}{(x+1)^{2}})^{1/2}}$
How do you go about simplifying this? DO you simplify each part individually by the 1/2 exponent? Thank you for any tips.
you can't do it individually because it is the same as:
$\displaystyle \sqrt{4-\frac{1}{(x+1)^2}}$
$\displaystyle \sqrt{a-b}\neq\sqrt{a}-\sqrt{b}$
to do this you have to subtract $\displaystyle 4-\frac{1}{(x-1)^2}$.can you do that?
As you were told above, the square root of a sum/difference is NOT equal to the sum/difference of the square roots. So you can't take each term in the numerator to the 1/2 power.
However, the square root of a product/quotient DOES equal the product/quotient of the square roots. So you CAN take the square root of the numerator and the square root of the denominator.