Question

Solve:$\sqrt{23+\sqrt{528}}=2\sqrt{3}+\sqrt{11}$

Answer 1

$\sqrt{23+\sqrt{528}}$
$=\sqrt{23+\sqrt{4\cdot 132}}$
$=\sqrt{23+2\sqrt{132}}$
$=\sqrt{23+2\sqrt{12}\sqrt{11}}$
$=\sqrt{11+12+2\sqrt{12}\sqrt{11}}$
$=\sqrt{(\sqrt{11}+\sqrt{12}{)}^2}$
$=\sqrt{11}+\sqrt{12}$
$=\sqrt{11}+\sqrt{4\cdot 3}$
$=\sqrt{11}+2\sqrt{3}$
$=2\sqrt{3}+\sqrt{11}$