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

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

Evaluate

$$\frac{\sqrt{2}}{6}+\frac{1}{3}\approx 0.569035594$$

Solution Steps

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

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

The square of \sqrt{2} is 2.

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

Multiply 3 and 2 to get 6.

$$\frac{\left(\sqrt{2}+1\right)\sqrt{2}}{6}$$

Use the distributive property to multiply \sqrt{2}+1 by \sqrt{2}.

$$\frac{\left(\sqrt{2}\right)^{2}+\sqrt{2}}{6}$$

The square of \sqrt{2} is 2.

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