Question

Simplify : $\frac{\sqrt{5}+\sqrt{3}}{\sqrt{80}+\sqrt{48}-\sqrt{45}-\sqrt{27}}$

Answer 1

$\frac{\sqrt{5}+\sqrt{3}}{\sqrt{80}+\sqrt{48}-\sqrt{45}-\sqrt{27}}=\frac{\sqrt{5}+\sqrt{3}}{\sqrt{16\times 5}+\sqrt{16\times 3}-\sqrt{9\times 5}-\sqrt{9\times 3}}$

$=\frac{\sqrt{5}+\sqrt{3}}{4\sqrt{5}+4\sqrt{3}-3\sqrt{5}-3\sqrt{3}}$

$=\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}+\sqrt{3}}$

$=1$