Solve 1/sqrt{2}+1/3sqrt{2}

$$\frac{ 1 }{ \sqrt{ 2 } } + \frac{ 1 }{ 3 \sqrt{ 2 } }$$

Evaluate

$$\frac{2\sqrt{2}}{3}\approx 0.942809042$$

Solution Steps

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}+\frac{1}{3\sqrt{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{2}}{2}+\frac{1}{3\sqrt{2}}$$

Rationalize the denominator of \frac{1}{3\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{3\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{6}$$

Combine \frac{\sqrt{2}}{2} and \frac{\sqrt{2}}{6} to get \frac{2}{3}\sqrt{2}.

$$\frac{2}{3}\sqrt{2}$$