Solve 7*sqrt{3/7}+3*sqrt{7/3}

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

Evaluate

$$2\sqrt{21}\approx 9.16515139$$

Solution Steps

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

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

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

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

The square of \sqrt{7} is 7.

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

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

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

Cancel out 7 and 7.

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

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

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

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

$$\sqrt{21}+3\times \frac{\sqrt{7}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

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

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

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

Cancel out 3 and 3.

$$\sqrt{21}+\sqrt{21}$$

Combine \sqrt{21} and \sqrt{21} to get 2\sqrt{21}.

$$2\sqrt{21}$$