Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 9 - Section 9.4 - Imaginary Numbers as Solutions of Quadratic Equations - Exercise Set: 15

Answer

$6-7i\sqrt{2}$

Work Step by Step

Using the properties of radicals and that $i=\sqrt{-1}$, then the given expression, $ 6-\sqrt{-98} ,$ is equivalent to \begin{array}{l}\require{cancel} 6-\sqrt{-1}\cdot\sqrt{98} \\\\= 6-i\cdot\sqrt{49\cdot2} \\\\= 6-i\cdot\sqrt{(7)^2\cdot2} \\\\= 6-i\cdot7\sqrt{2} \\\\= 6-7i\sqrt{2} .\end{array}
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