$${\sqrt{{\frac{{\mathtt{4}}}{{\mathtt{6}}}}}}$$
1. Change the $${\sqrt{}}$$ so that the numerator and dominator are $${\sqrt{}}$$s by themselves: $${\frac{{\sqrt{{\mathtt{4}}}}}{{\sqrt{{\mathtt{6}}}}}}$$
2. Take the $${\sqrt{}}$$s of the numerator and the dominator and simplify them as much as you can: $${\frac{{\mathtt{2}}}{{\sqrt{{\mathtt{6}}}}}}$$
3. Since $${\sqrt{{\mathtt{6}}}}$$ cannot be simplified any further and you cannot have a $${\sqrt{}}$$ in in the dominator, the $${\sqrt{}}$$ needs to come out of the dominator. The easiest way to do that is to multiply the numerator and dominator by $${\sqrt{{\mathtt{6}}}}$$:
$${\frac{{\mathtt{2}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6}}}}}{{\mathtt{6}}}}$$
4. Simplify the the fraction.
a. Break the fraction up: $${\frac{{\mathtt{2}}}{{\mathtt{6}}}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6}}}}$$
b. Reduce the fraction $${\frac{{\mathtt{2}}}{{\mathtt{6}}}}$$ and leave $${\sqrt{{\mathtt{6}}}}$$ alone: $${\frac{{\mathtt{1}}}{{\mathtt{3}}}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{6}}}}$$
c. Multiply the fraction $${\frac{{\mathtt{1}}}{{\mathtt{3}}}}$$ and $${\sqrt{{\mathtt{6}}}}$$: $${\frac{{\sqrt{{\mathtt{6}}}}}{{\mathtt{3}}}}$$
$${\sqrt{{\frac{{\mathtt{4}}}{{\mathtt{6}}}}}}$$ in is simplied form is $${\frac{{\sqrt{{\mathtt{6}}}}}{{\mathtt{3}}}}$$
If you take $${\sqrt{{\mathtt{6}}}}$$ and divide it by $${\mathtt{3}}$$, you get a decimal number that goes on forever: 0.816496580927726...
