<s>[INST] Simplifying a radical? How would I simplify the following two radicals.
$$\sqrt{\frac{X^3}{50}}$$ 
For my answer I got $\frac{X^2}{50X}$ but I am not sure if this is correct.
My second question is how would I simplify $\sqrt{\frac{1}{12}}$
 [/INST] No, your simplification is incorrect.
The first radical only makes sense if $x\geq 0$. Assuming this is the case, remember that:


*

*If $a$ and $b$ are both nonnegative, then $\sqrt{ab}=\sqrt{a}\sqrt{b}$, and $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$. 

*$(\sqrt{a})^2 = a$ for any $a\geq 0$.
So:
$$\sqrt{\frac{x^3}{50}} = \frac{\sqrt{x^3}}{\sqrt{50}} = \frac{\sqrt{x^2}\sqrt{x}}{\sqrt{25}\sqrt{2}} = \frac{x\sqrt{x}}{5\sqrt{2}} = \frac{x\sqrt{x}\sqrt{2}}{5\sqrt{2}\sqrt{2}} = \frac{x\sqrt{2x}}{10}.$$
There are other ways of expressing it as well.
For the second, $12 = 4\times 3$, so 
$$\sqrt{12}=\sqrt{4}\sqrt{3} = 2\sqrt{3}.$$
Can you take it from there?
</s>