Chapter 8 - Section 8.2 - Multiplying and Dividing Radicals - Exercise Set - Page 585: 7

$\sqrt{\dfrac{10}{21}}$

Using $\sqrt{x}\cdot\sqrt{y}=\sqrt{xy}$ or the product rule of radicals, the given expression, $ \sqrt{\dfrac{2}{3}}\cdot\sqrt{\dfrac{5}{7}} ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt{\dfrac{2}{3}\cdot\dfrac{5}{7}} \\\\= \sqrt{\dfrac{10}{21}} .\end{array}