Solve sqrt{5/3}3/sqrt{7}

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

Evaluate

$$\frac{\sqrt{105}}{7}\approx 1.463850109$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{5}{3}} as the division of square roots \frac{\sqrt{5}}{\sqrt{3}}.

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

Rationalize the denominator of \frac{\sqrt{5}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

To multiply \sqrt{5} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{\sqrt{15}}{3}\times \frac{3}{\sqrt{7}}$$

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

$$\frac{\sqrt{15}}{3}\times \frac{3\sqrt{7}}{\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{\sqrt{15}}{3}\times \frac{3\sqrt{7}}{7}$$

Multiply \frac{\sqrt{15}}{3} times \frac{3\sqrt{7}}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\sqrt{15}\times 3\sqrt{7}}{3\times 7}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\sqrt{7}\sqrt{15}}{7}$$

To multiply \sqrt{7} and \sqrt{15}, multiply the numbers under the square root.

$$\frac{\sqrt{105}}{7}$$