square root of $\frac{2+\sqrt{3}}{4}$ 
Find the square root of $\frac{2+\sqrt{3}}{4}$.

Attempt:
I'm thinking of equating it to $a + bi$. And then finding the root. Is that right?

$\frac{2+\sqrt{3}}{4}$ is a positive number so it has a real square root.
Notice first that:
$$\sqrt{\dfrac{2+\sqrt{3}}{4}}=\dfrac{\sqrt{2+\sqrt{3}}}{2}$$
 so what you have to find is $\sqrt{2+\sqrt{3}}$. A technique is to try to find what are $a,b\in\mathbb{R}$ where $2+\sqrt{3}=(a+b)^2$ so that $2+\sqrt{3}=|a+b|$.
You have $$(a+b)^2=a^2+b^2+2ab$$.
The technique in such cases is to try to get $a^2+b^2=2$ and $2ab=\sqrt{3}$.
Notice that $b=\frac{\sqrt{3}}{2a}$
If you put it in $a^2+b^2=2$ you'll have an equation with one variable $a$.
