Question

$sqrt{7-4sqrt{3}}+sqrt{3}$

Answer 1

$7-4sqrt{3}=4-2cdot{2}sqrt{3}+3=(2-sqrt{3})^{2}$
$sqrt{7-4sqrt{3}}+sqrt{3}=|2-sqrt{3}|+sqrt{3}=2-sqrt{3}+sqrt{3}=2$
Так как $2-sqrt{3}>0$, то модуль $|2-sqrt{3}|=2-sqrt{3}$

Answer 2

$sqrt{7-4sqrt{3}}+sqrt{3}=sqrt{3+4-4sqrt{3}}+sqrt{3}=\sqrt{2^2-2*2sqrt{3}+(sqrt3)^2}+sqrt{3}=sqrt{(2-sqrt{3})^2}+sqrt{3}=\|2-sqrt3|+sqrt3=2$