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Simplify the expression
\frac{1}{\sqrt{36}} - \sqrt{27} - \frac{1}{\sqrt{27}} - \sqrt{18} + \frac{1}{\sqrt{18}} - \sqrt{9}

 Aug 18, 2024
 #1
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\(\frac{1}{\sqrt{36}} - \sqrt{27} - \frac{1}{\sqrt{27}} - \sqrt{18} + \frac{1}{\sqrt{18}} - \sqrt{9}\)

is equal to

\(-\frac{17}{6} + \frac{1}{3\sqrt2} - 3\sqrt2 - \frac{1}{3\sqrt{3}} - 3\sqrt{3}\)

rationalizing the denominators and simplifying gives
\(-\frac{17}{6} + \frac{\sqrt2}{6} - 3\sqrt2 - \frac{\sqrt{3}}{9} - 3\sqrt{3}\)

 Aug 18, 2024

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