<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] Hint. Note that
$$(2\pm\sqrt{2})=\sqrt{(2\pm\sqrt{2})^2}=\sqrt{6\pm 4\sqrt{2}}.$$
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