Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Skills Handbook - Squaring Numbers and Finding Square Roots - Exercises: 17

Answer

$b=6\text{ or }b=-6$

Work Step by Step

We start with the given equation: $8^2+b^2=10^2$ To simplify each of the constants being squared, we multiply them by themselves: $64+b^2=100$ In order to get the term with $b$ by itself, we subtract $64$ from both sides of the equation: $$64-64+b^2=100-64$$$$b^2=36$$To solve the equation $b^2=36$, we must perform the opposite operation of squaring, which is taking the square root, in order to clear the exponent: $$b^2=36$$$$\sqrt {b^2}=\sqrt {36}$$$$b=\pm6$$$$b=6\text{ or }b=-6$$
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