Solve 2/7*sqrt{2}frac{7+sqrt{2}}{7+sqrt{2}}

$$\frac { 2 } { 7 \cdot \sqrt { 2 } } \frac { 7 + \sqrt { 2 } } { 7 + \sqrt { 2 } }$$

Evaluate

$$\frac{\sqrt{2}}{7}\approx 0.202030509$$

Solution Steps

Divide 7+\sqrt{2} by 7+\sqrt{2} to get 1.

$$\frac{2}{7\sqrt{2}}\times 1$$

Rationalize the denominator of \frac{2}{7\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{2\sqrt{2}}{7\left(\sqrt{2}\right)^{2}}\times 1$$

The square of \sqrt{2} is 2.

$$\frac{2\sqrt{2}}{7\times 2}\times 1$$

Cancel out 2 in both numerator and denominator.

$$\frac{\sqrt{2}}{7}\times 1$$

Express \frac{\sqrt{2}}{7}\times 1 as a single fraction.

$$\frac{\sqrt{2}}{7}$$