Unrationalize Denominator

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What is the method to unrationalize or reverse a rationalized fraction?

For example: How do you simplify $\frac{1}{2\sqrt\frac{1}{2}}$ = $\frac{1}{\sqrt{2}}$

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1 Answer

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$$\frac{1}{2\sqrt{\frac{1}{2}}}=\frac{1}{\sqrt{4}\sqrt{\frac{1}{2}}}=\frac{1}{\sqrt{\frac{4}{2}}}=\frac{1}{\sqrt{2}}$$ Now you can multiply by "1": $$\frac{1}{\sqrt{2}}\frac{1}{1}=\frac{1}{\sqrt{2}} \frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{(\sqrt{2})^2}=\frac{\sqrt{2}}{2}$$

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