(1/ $\sqrt{\ 2}$) + (1/ $\sqrt{\ 18}$) - (1/ $\sqrt{\ 8}$ )

asked by guest
on Mar 23, 2025 at 8:39 pm



You asked:

Evaluate the expression: \(\frac{1}{\sqrt{2}} + \frac{1}{\sqrt{18}} - \frac{1}{\sqrt{8}}\)

MathBot Answer:

\[\frac{1}{\sqrt{2}} + \frac{1}{\sqrt{18}} - \frac{1}{\sqrt{8}} = \frac{5 \sqrt{2}}{12} \approx 0.58925565098878960366737030175404\]

\[\begin{aligned}\frac{1}{\sqrt{2}} + \frac{1}{\sqrt{18}} - \frac{1}{\sqrt{8}}&=\frac{1}{2} \cdot \sqrt{2} + \frac{1}{\sqrt{18}} - \frac{1}{\sqrt{8}}\\&=\frac{1}{2} \cdot \sqrt{2} + \frac{1}{3 \cdot \sqrt{2}} - \frac{1}{\sqrt{8}}\\&=\frac{1}{2} \cdot \sqrt{2} + \frac{1}{6} \cdot \sqrt{2} - \frac{1}{\sqrt{8}}\\&=\frac{1}{2} \cdot \sqrt{2} + \frac{1}{6} \cdot \sqrt{2} - \frac{1}{2 \cdot \sqrt{2}}\\&=\frac{1}{2} \cdot \sqrt{2} + \frac{1}{6} \cdot \sqrt{2} - \frac{1}{4} \cdot \sqrt{2}\\&=\frac{2}{3} \cdot \sqrt{2} - \frac{1}{4} \cdot \sqrt{2}\\&=\frac{5}{12} \cdot \sqrt{2}\end{aligned}\]

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