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,

$$\sqrt{ 14 \pm 4 \sqrt{10}} = \sqrt{10} \pm 2 $$
since $\sqrt{10} \pm 2>0 $ and $(\sqrt{10} \pm 2)^2 =  14 \pm 4 \sqrt{10} $.
