Chapter 10 - Exponents and Radicals - 10.8 The Complex Numbers - 10.8 Exercise Set - Page 686: 39

$-18$

Using $i=\sqrt{-1},$ $i^2=-1,$ and the properties of radicals, the given expression, $ \sqrt{-36}\sqrt{-9} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt{-1}\sqrt{36}\cdot\sqrt{-1}\sqrt{9} \\\\= i\sqrt{(6)^2}\cdot i\sqrt{(3)^2} \\\\= 6i\cdot3i \\\\= 18i^2 \\\\= 18(-1) \\\\= -18 .\end{array}