Express $\frac{\frac{3}{5}}{8}$ as a single fraction.
$$\sqrt{\frac{3}{5\times 8}\times 6}$$
Multiply $5$ and $8$ to get $40$.
$$\sqrt{\frac{3}{40}\times 6}$$
Express $\frac{3}{40}\times 6$ as a single fraction.
$$\sqrt{\frac{3\times 6}{40}}$$
Multiply $3$ and $6$ to get $18$.
$$\sqrt{\frac{18}{40}}$$
Reduce the fraction $\frac{18}{40}$ to lowest terms by extracting and canceling out $2$.
$$\sqrt{\frac{9}{20}}$$
Rewrite the square root of the division $\sqrt{\frac{9}{20}}$ as the division of square roots $\frac{\sqrt{9}}{\sqrt{20}}$.
$$\frac{\sqrt{9}}{\sqrt{20}}$$
Calculate the square root of $9$ and get $3$.
$$\frac{3}{\sqrt{20}}$$
Factor $20=2^{2}\times 5$. Rewrite the square root of the product $\sqrt{2^{2}\times 5}$ as the product of square roots $\sqrt{2^{2}}\sqrt{5}$. Take the square root of $2^{2}$.
$$\frac{3}{2\sqrt{5}}$$
Rationalize the denominator of $\frac{3}{2\sqrt{5}}$ by multiplying numerator and denominator by $\sqrt{5}$.
