1Cademy - Simplifying $$\frac{1}{\sqrt[4]{2}}$$

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Rationalizing the Denominator

Example

Simplifying $\frac{1}{\sqrt[4]{2}}$

To simplify the expression $\frac{1}{\sqrt[4]{2}}$ , rationalize the denominator by multiplying both the numerator and the denominator by $\sqrt[4]{2^3}$ . The radical in the denominator has one factor of 2, so multiplying by $\sqrt[4]{2^3}$ provides the 3 additional factors needed to complete a perfect fourth power. This results in $\frac{1 \cdot \sqrt[4]{2^3}}{\sqrt[4]{2} \cdot \sqrt[4]{2^3}} = \frac{\sqrt[4]{8}}{\sqrt[4]{2^4}}$ . Simplifying the fourth root in the denominator yields the final expression $\frac{\sqrt[4]{8}}{2}$ .