+205 Simplify: $\frac{1}{\sqrt{2}+\frac{1}{\sqrt{8}+\sqrt{200}+\frac{1}{\sqrt{18}}}}$.
+600 Annoying - it boils down to $\boxed{\frac{73\sqrt{2}}{152}}$.
+239 Correct thedudemanguyperson...!
\(\frac{1}{\sqrt{2}+\frac{1}{\sqrt{8}+\sqrt{200}+\frac{1}{\sqrt{18}}}}\)
\(\frac{1}{\sqrt{8}+\sqrt{200}+\frac{1}{\sqrt{18}}}=\frac{3\sqrt{2}}{73} \)
\(=\frac{1}{\sqrt{2}+\frac{3\sqrt{2}}{73}}\)
\(\sqrt{2}+\frac{3\sqrt{2}}{73}:{\frac{76\sqrt{2}}{73}}\)
\(=\frac{1}{\frac{76\sqrt{2}}{73}}\)
\(\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{1}{\frac{b}{c}}=\frac{c}{b}\)
\(=\frac{73}{76\sqrt{2}}\)
\(Rationalize \frac{73}{76\sqrt{2}}:\frac{73\sqrt{2}}{152}\)
\(=\frac{73\sqrt{2}}{152}\)
