Solve frac{sqrt{7}}{7sqrt{3}}

$$\frac { \sqrt { 7 } } { 7 \sqrt { 3 } }$$

Evaluate

$$\frac{\sqrt{21}}{21}\approx 0.21821789$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{7}}{7\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{\sqrt{7}\sqrt{3}}{7\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{\sqrt{7}\sqrt{3}}{7\times 3}$$

To multiply \sqrt{7} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\sqrt{21}}{7\times 3}$$

Multiply 7 and 3 to get 21.

$$\frac{\sqrt{21}}{21}$$