Solve 2sqrt{3}divsqrt{7/3}*sqrt{7/5}

$$2 \sqrt{ 3 } \div \sqrt{ \frac{ 7 }{ 3 } } \times \sqrt{ \frac{ 7 }{ 5 } }$$

Evaluate

$$\frac{6\sqrt{5}}{5}\approx 2.683281573$$

Solution Steps

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

$$\frac{2\sqrt{3}}{\frac{\sqrt{7}}{\sqrt{3}}}\sqrt{\frac{7}{5}}$$

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

$$\frac{2\sqrt{3}}{\frac{\sqrt{7}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}}\sqrt{\frac{7}{5}}$$

The square of \sqrt{3} is 3.

$$\frac{2\sqrt{3}}{\frac{\sqrt{7}\sqrt{3}}{3}}\sqrt{\frac{7}{5}}$$

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

$$\frac{2\sqrt{3}}{\frac{\sqrt{21}}{3}}\sqrt{\frac{7}{5}}$$

Divide 2\sqrt{3} by \frac{\sqrt{21}}{3} by multiplying 2\sqrt{3} by the reciprocal of \frac{\sqrt{21}}{3}.

$$\frac{2\sqrt{3}\times 3}{\sqrt{21}}\sqrt{\frac{7}{5}}$$

Rationalize the denominator of \frac{2\sqrt{3}\times 3}{\sqrt{21}} by multiplying numerator and denominator by \sqrt{21}.

$$\frac{2\sqrt{3}\times 3\sqrt{21}}{\left(\sqrt{21}\right)^{2}}\sqrt{\frac{7}{5}}$$

The square of \sqrt{21} is 21.

$$\frac{2\sqrt{3}\times 3\sqrt{21}}{21}\sqrt{\frac{7}{5}}$$

Multiply 2 and 3 to get 6.

$$\frac{6\sqrt{3}\sqrt{21}}{21}\sqrt{\frac{7}{5}}$$

Factor 21=3\times 7. Rewrite the square root of the product \sqrt{3\times 7} as the product of square roots \sqrt{3}\sqrt{7}.

$$\frac{6\sqrt{3}\sqrt{3}\sqrt{7}}{21}\sqrt{\frac{7}{5}}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{6\times 3\sqrt{7}}{21}\sqrt{\frac{7}{5}}$$

Multiply 6 and 3 to get 18.

$$\frac{18\sqrt{7}}{21}\sqrt{\frac{7}{5}}$$

Divide 18\sqrt{7} by 21 to get \frac{6}{7}\sqrt{7}.

$$\frac{6}{7}\sqrt{7}\sqrt{\frac{7}{5}}$$

Rewrite the square root of the division \sqrt{\frac{7}{5}} as the division of square roots \frac{\sqrt{7}}{\sqrt{5}}.

$$\frac{6}{7}\sqrt{7}\times \frac{\sqrt{7}}{\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{7}}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{6}{7}\sqrt{7}\times \frac{\sqrt{7}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{6}{7}\sqrt{7}\times \frac{\sqrt{7}\sqrt{5}}{5}$$

To multiply \sqrt{7} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{6}{7}\sqrt{7}\times \frac{\sqrt{35}}{5}$$

Multiply \frac{6}{7} times \frac{\sqrt{35}}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{6\sqrt{35}}{7\times 5}\sqrt{7}$$

Multiply 7 and 5 to get 35.

$$\frac{6\sqrt{35}}{35}\sqrt{7}$$

Express \frac{6\sqrt{35}}{35}\sqrt{7} as a single fraction.

$$\frac{6\sqrt{35}\sqrt{7}}{35}$$

Factor 35=7\times 5. Rewrite the square root of the product \sqrt{7\times 5} as the product of square roots \sqrt{7}\sqrt{5}.

$$\frac{6\sqrt{7}\sqrt{5}\sqrt{7}}{35}$$

Multiply \sqrt{7} and \sqrt{7} to get 7.

$$\frac{6\times 7\sqrt{5}}{35}$$

Multiply 6 and 7 to get 42.

$$\frac{42\sqrt{5}}{35}$$

Divide 42\sqrt{5} by 35 to get \frac{6}{5}\sqrt{5}.

$$\frac{6}{5}\sqrt{5}$$