<s>[INST] Problem with $\frac{\sqrt{6+4\sqrt{2}}}{4+2\sqrt{2}}$ How to simplify $$\frac{\sqrt{6+4\sqrt{2}}}{4+2\sqrt{2}}?$$
Rationalise the denominator 
$$\frac{\sqrt{6+4\sqrt{2}}}{4}(2-\sqrt{2})$$
This is still not simplify.
 [/INST] We have $$6+4\sqrt{2}=4+2+4\sqrt{2}$$ so $$2\sqrt{6+4\sqrt{2}}=4+2\sqrt{2}$$ and we get
$$\frac{\sqrt{6+4\sqrt{2}}}{4+2\sqrt{2}}=\frac{1}{2}$$
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