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: 20

Answer

$a\approx13.2\text{ or }a\approx-13.2$

Work Step by Step

We start with the given equation: $20^2=15^2+a^2$ To simplify each of the constants being squared, we multiply them by themselves: $400=225+a^2$ In order to get the term with $a$ by itself, we subtract $225$ from both sides of the equation: $$400-225=225-225+a^2$$$$175=a^2$$ To solve the equation $175=a^2$, we must perform the opposite operation of squaring, which is taking the square root, in order to clear the exponent: $$175=a^2$$$$\sqrt {175}=\sqrt {a^2}$$$$a\approx\pm13.2$$$$a\approx13.2\text{ or }a\approx-13.2$$
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