TITLE: How would you show that $\sqrt{14+4\sqrt{10}} - \sqrt{14-4\sqrt{10}} = 4$?
QUESTION [5 upvotes]: 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,

REPLY [3 votes]: This was quite easy sum , here I used the general solution for (a+2b^1/2)^1/2=x^1/2 +y^1/2