Chapter 10 - Exponents and Radicals - 10.3 Multiplying Radical Expressions - 10.3 Exercise Set - Page 647: 60

$5\sqrt{14}$

Using the properties of radicals, the given expression, $ \sqrt{10}\sqrt{35} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt{10(35)} \\\\= \sqrt{2\cdot5(5\cdot7)} \\\\= \sqrt{(5)^2\cdot2\cdot7} \\\\= \sqrt{(5)^2\cdot14} \\\\= 5\sqrt{14} \end{array}