How do you rationalize the denominator $\sqrt{\frac{5}{6}}$ $sqrt(5/6)$ ?

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How do you rationalize the denominator $\sqrt{\frac{5}{6}}$ $sqrt(5/6)$ ?

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Answer 1 · 2015-05-31T12:05:11

Multiply both numerator and denominator by $\sqrt{6}$ $sqrt(6)$ :

$\sqrt{\frac{5}{6}} = \frac{\sqrt{5}}{\sqrt{6}} = \frac{\sqrt{5}}{\sqrt{6}} \cdot \frac{\sqrt{6}}{\sqrt{6}}$ $sqrt(5/6) = sqrt(5)/sqrt(6) = sqrt(5)/sqrt(6)*sqrt(6)/sqrt(6)$

$= \frac{\sqrt{5} \sqrt{6}}{{(\sqrt{6})}^{2}} = \frac{\sqrt{5 \cdot 6}}{6}$ $= (sqrt(5)sqrt(6))/((sqrt(6))^2) = (sqrt(5*6))/6$

$= \frac{\sqrt{30}}{6}$ $=sqrt(30)/6$

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How do you rationalize the denominator $\sqrt{\frac{5}{6}}$ $sqrt(5/6)$ ?

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