Solve frac{frac{sqrt{7}}{4}}{sqrt{2}}

$$\frac { \frac { \sqrt { 7 } } { 4 } } { \sqrt { 2 } }$$

Evaluate

$$\frac{\sqrt{14}}{8}\approx 0.467707173$$

Solution Steps

Express \frac{\frac{\sqrt{7}}{4}}{\sqrt{2}} as a single fraction.

$$\frac{\sqrt{7}}{4\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{7}}{4\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{7}\sqrt{2}}{4\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{7}\sqrt{2}}{4\times 2}$$

To multiply \sqrt{7} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{14}}{4\times 2}$$

Multiply 4 and 2 to get 8.

$$\frac{\sqrt{14}}{8}$$