Question

Evaluate $\frac{15}{\sqrt{10}+\sqrt{20}+\sqrt{40}-\sqrt{5}-\sqrt{80}}$, it us given that $\sqrt{5}=2.236$ and $\sqrt{10}=3.162$

Answer 1

$Given\sqrt{5}=2.236\sqrt{10}=3.162Tofind\frac{15}{\sqrt{10}+\sqrt{20}+\sqrt{40}-\sqrt{5}-\sqrt{80}}=\frac{15}{\sqrt{10}+\sqrt{4\times 5}+\sqrt{4\times 10}-\sqrt{5}-\sqrt{16\times 5}}=\frac{15}{\sqrt{10}+2\sqrt{5}+2\sqrt{10}-\sqrt{5}-4\sqrt{5}}=\frac{15}{3\sqrt{10}-3\sqrt{5}}=\frac{5\times 3}{3(\sqrt{10}-\sqrt{5})}=\frac{5}{\sqrt{10}-\sqrt{5}}=\frac{5}{3.162-2.236}=\frac{5}{0.926}=5.39$