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?

HINT: Square both sides
 $$ (\sqrt{43 + 24 \sqrt{3}})^2  = 16 + 9(3) + 24 \sqrt{3},$$
 $$  43 + 24 \sqrt{3} = 43 + 24\sqrt{3}.$$
NOTE $(a+b)^2 = a^2 + 2ab + b^2$
