Question

Root27 + root45 whole divided by root3 + root5

Answer 1

Given expression,

\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}}

(\because \sqrt{a\times b}=\sqrt{a}\times \sqrt{b})

=\frac{\sqrt{5}+\sqrt{3}}{4(\sqrt{5}+\sqrt{3})-3(\sqrt{5}+\sqrt{3})}

=\frac{\sqrt{5}+\sqrt{3}}{(\sqrt{5}+\sqrt{3})(4-3)}

=1