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Rationalize the denominator: $\frac{1}{\sqrt{8}+\sqrt{50}+\sqrt{18}}$.

 Jan 13, 2018

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 #1
avatar+8071 
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\(\quad\,\frac{1}{\sqrt{8}+\sqrt{50}+\sqrt{18}} \\~\\ =\,\frac{1}{2\sqrt{2}\,+\,5\sqrt{2}\,+\,3\sqrt{2}} \\~\\ =\,\frac{1}{10\sqrt{2}} \\~\\ =\,\frac{1\,\cdot\,\sqrt2}{10\sqrt2\,\cdot\,\sqrt2} \\~\\ =\,\frac{\sqrt2}{10\,\cdot\,2} \\~\\ =\,\frac{\sqrt2}{20}\)

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 Jan 13, 2018
 #1
avatar+8071 
+1
Best Answer

\(\quad\,\frac{1}{\sqrt{8}+\sqrt{50}+\sqrt{18}} \\~\\ =\,\frac{1}{2\sqrt{2}\,+\,5\sqrt{2}\,+\,3\sqrt{2}} \\~\\ =\,\frac{1}{10\sqrt{2}} \\~\\ =\,\frac{1\,\cdot\,\sqrt2}{10\sqrt2\,\cdot\,\sqrt2} \\~\\ =\,\frac{\sqrt2}{10\,\cdot\,2} \\~\\ =\,\frac{\sqrt2}{20}\)

hectictar Jan 13, 2018

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