How would you show that $\sqrt{14+4\sqrt{10}} - \sqrt{14-4\sqrt{10}} = 4$? I've recently seen a Highschool problem and I was wondering, how would you show that
$$\sqrt{14+4\sqrt{10}} - \sqrt{14-4\sqrt{10}} = 4$$
Thank you for your time,

Denote $\sqrt{14+4\sqrt{10}}=a, \sqrt{14-4\sqrt{10}}=b$, then
$$a^2+b^2=28, ab=6$$
So $(a-b)^2=16$ and $a-b=4$.
