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### Strategies to denest nested radicals.

I have recently read some passage about nested radicals, I'm deeply impressed by them. Simple nested radicals $\sqrt{2+\sqrt{2}}$,$\sqrt{3-2\sqrt{2}}$ which the later can be denested into $1-\sqrt{2}$....
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### Simplifying $\sqrt{4+2\sqrt{3}}+\sqrt{4-2\sqrt{3}}$

How do I simplify $\sqrt{(4+2\sqrt{3})}+\sqrt{(4-2\sqrt{3})}$? I've tried to make it $x$ and square both sides but I got something extremely complicated and it didn't look right. I got $2\sqrt{3}$ ...
### Simplifying $\sqrt[4]{161-72 \sqrt{5}}$
$$\sqrt[4]{161-72 \sqrt{5}}$$ I tried to solve this as follows: the resultant will be in the form of $a+b\sqrt{5}$ since 5 is a prime and has no other factors other than 1 and itself. Taking this ...