Evaluate: $\frac{1}{4} - \frac{1}{4 \sqrt{2}}$

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Solution

$\begin{matrix} \frac{1}{4} - \frac{1}{4 \sqrt{2}} = \frac{\sqrt{2} - 1}{4 \sqrt{2}} = \frac{\begin{matrix} (\sqrt{2} - 1) \end{matrix}}{4 \sqrt{2}} . \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{2} (\sqrt{2} - 1)}{4.2} = \frac{2 - \sqrt{2}}{8} \end{matrix}$

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