Chapter 8 - Section 8.2 - Multiplying and Dividing Radicals - Exercise Set - Page 585: 8

$\sqrt{\dfrac{3}{7}}$

Using $\sqrt{x}\cdot\sqrt{y}=\sqrt{xy}$ or the product rule of radicals, the given expression, $ \sqrt{\dfrac{3}{5}}\cdot\sqrt{\dfrac{5}{7}} ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt{\dfrac{3}{5}\cdot\dfrac{5}{7}} \\\\= \sqrt{\dfrac{3}{\cancel{5}}\cdot\dfrac{\cancel{5}}{7}} \\\\= \sqrt{\dfrac{3}{7}} .\end{array}