How do you rationalize $\sqrt{\frac{5}{8}}$ $sqrt(5/8)$ ?

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How do you rationalize $\sqrt{\frac{5}{8}}$ $sqrt(5/8)$ ?

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Answer 1 · 2015-05-17T21:54:28

Write it as: $\frac{\sqrt{5}}{\sqrt{8}}$ $sqrt(5)/sqrt(8)$
then multiply and divide by $\sqrt{8}$ $sqrt(8)$ to get:
$\frac{\sqrt{5}}{\sqrt{8}} \cdot \frac{\sqrt{8}}{\sqrt{8}} = \frac{\sqrt{5} \sqrt{8}}{8} =$ $sqrt(5)/sqrt(8)*sqrt(8)/sqrt(8)=(sqrt(5)sqrt(8))/8=$
$= \frac{\sqrt{5} \sqrt{4 \cdot 2}}{8} = 2 \frac{\sqrt{5} \sqrt{2}}{8} = \frac{\sqrt{5} \sqrt{2}}{4} = \frac{\sqrt{10}}{4}$ $=(sqrt(5)sqrt(4*2))/8=2(sqrt(5)sqrt(2))/8=(sqrt(5)sqrt(2))/4=sqrt(10)/4$

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How do you rationalize $\sqrt{\frac{5}{8}}$ $sqrt(5/8)$ ?

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