# Chapter 7 - Section 7.7 - Complex Numbers - Exercise Set - Page 570: 5

$3i\sqrt{2}$

#### Work Step by Step

Factor the radicand so that one factor $-1$ to obtain: $=\sqrt{18(-1)} \\=\sqrt{2(9)(-1)} \\=\sqrt{2(3^2)(-1)}$ RECALL: (1) $\sqrt{abc} = \sqrt{a} \cdot \sqrt{b} \cdot \sqrt{c}$ (2) $\sqrt{-1} = i$ Use rule (1) above to obtain: $=\sqrt{2} \cdot \sqrt{3^2} \cdot \sqrt{-1} \\=\sqrt{2} \cdot 3 \sqrt{-1} \\=3\sqrt{2} \cdot \sqrt{-1}$ Use rule (2) above to obtain: $=3\sqrt{2} \cdot i \\=3i\sqrt{2}$

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