# Chapter 10 - Exponents and Radicals - 10.8 The Complex Numbers - 10.8 Exercise Set: 40

$-28$

#### Work Step by Step

Using $i=\sqrt{-1},$ $i^2=-1,$ and the properties of radicals, the given expression, $\sqrt{-49}\sqrt{-16} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt{-1}\sqrt{49}\cdot\sqrt{-1}\sqrt{16} \\\\= i\sqrt{49}\cdot i\sqrt{16} \\\\= i\sqrt{(7)^2}\cdot i\sqrt{(4)^2} \\\\= 7i\cdot 4i \\\\= 28i^2 \\\\= 28(-1) \\\\= -28 .\end{array}

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