Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 8 - Complex Numbers, Polar Equations, and Parametric Equations - Section 8.1 Complex Numbers - 8.1 Exercises - Page 357: 46

Answer

$\frac{1}{3}$

Work Step by Step

$\frac{\sqrt -8}{\sqrt -72}=\frac{i\sqrt 8}{i\sqrt 72}=\frac{i}{i}\times\frac{\sqrt 8}{\sqrt 72}=1\times\sqrt \frac{8}{72}=\sqrt \frac{8}{72}=\sqrt \frac{1}{9}=\frac{1}{3}$ We know that $\sqrt \frac{1}{9}=\frac{1}{3}$, because $(\frac{1}{3})^{2}=\frac{1}{9}$. We know that $\sqrt -1=i$, because $i^{2}=-1$.
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