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 - Page 889: 19


$p=5\text{ or }p=-5$

Work Step by Step

We start with the given equation: $p^2+12^2=13^2$ To simplify each of the constants being squared, we multiply them by themselves: $p^2+144=169$ In order to get the term with $p$ by itself, we subtract $144$ from both sides of the equation: $$p^2+144-144=169-144$$$$p^2=25$$ To solve the equation $p^2=25$, we must perform the opposite operation of squaring, which is taking the square root, in order to clear the exponent: $$p^2=25$$$$\sqrt {p^2}=\sqrt {25}$$$$p=\pm5$$$$p=5\text{ or }p=-5$$
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