Solve (3)sqrt{7/3}

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

Evaluate

$$\sqrt{21}\approx 4.582575695$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{7}{3}} as the division of square roots \frac{\sqrt{7}}{\sqrt{3}}.

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

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

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

The square of \sqrt{3} is 3.

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

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

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

Cancel out 3 and 3.

$$\sqrt{21}$$