Having trouble simplyfing radicals of this sort I'm studying radicals and rational exponents. I'm having lots of hardships with problems of this sort: prove $$\sqrt{43+24\sqrt{3}}=4+3\sqrt{3}$$ I keep going around and around experimenting with factoring. I can't seem to be able to prove this one in particular. Am I missing any common practice in regards to solving these and thus complicating it further? Is there any thing in particular I should always have in mind, or is this just lack of practice?

Starting with $$\sqrt{43+24\sqrt{3}}=4+3\sqrt{3}$$
you can square both sides to get
$$
\begin{eqnarray}
43+24\sqrt{3} & = & (4+3\sqrt{3})^2 \\
& = & (4+3\sqrt{3})(4+3\sqrt{3}) \\
& = & 16+12\sqrt{3}+12\sqrt{3}+27 \\
& = & 43+24\sqrt{3} \\
\end{eqnarray}
$$
