Question

Aratati ca numarul $\sqrt{7+4 \sqrt{3} } - \sqrt{3}$  este natural.

Answer 1

$\sqrt{7+\sqrt{48}$ - $\sqrt{3}$ 
7=A
B= $\sqrt{48}$
C=$\sqrt{A ^{2} - \sqrt{B}$
C=$\sqrt{7 ^{2} - 48$
C=1
$\sqrt{ \frac{7+1}{2}} + \sqrt{ \frac{7-1}{2} } = 2 + \sqrt{3}$
$2 + \sqrt{3} - \sqrt{3} = 2$