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avatar+204 

Simplify: $\frac{1}{\sqrt{2}+\frac{1}{\sqrt{8}+\sqrt{200}+\frac{1}{\sqrt{18}}}}$.

 Feb 24, 2021
 #1
avatar+602 
+1

Annoying - it boils down to $\boxed{\frac{73\sqrt{2}}{152}}$.

 Feb 24, 2021
 #2
avatar+235 
0

Correct thedudemanguyperson...!

\(\frac{1}{\sqrt{2}+\frac{1}{\sqrt{8}+\sqrt{200}+\frac{1}{\sqrt{18}}}}\)

                                        \(​​​​\frac{1}{\sqrt{8}+\sqrt{200}+\frac{1}{\sqrt{18}}}=\frac{3\sqrt{2}}{73} \)

\(=\frac{1}{\sqrt{2}+\frac{3\sqrt{2}}{73}}\)

                                        \(\sqrt{2}+\frac{3\sqrt{2}}{73}:{\frac{76\sqrt{2}}{73}}\)                  

\(=\frac{1}{\frac{76\sqrt{2}}{73}}\)

                                      \(\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{1}{\frac{b}{c}}=\frac{c}{b}\)

\(=\frac{73}{76\sqrt{2}}\)

                                      \(Rationalize \frac{73}{76\sqrt{2}}:\frac{73\sqrt{2}}{152}\)

\(=\frac{73\sqrt{2}}{152}\)

 

cheekycheekycheeky

 Feb 24, 2021

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