## Geometry: Common Core (15th Edition)

Published by Prentice Hall

# Skills Handbook - Squaring Numbers and Finding Square Roots - Exercises - Page 889: 18

#### Answer

$c\approx6.4\text{ or }c\approx-6.4$

#### Work Step by Step

We start with the given equation: $5^2+4^2=c^2$ To simplify each of the constants being squared, we multiply them by themselves: $25+16=c^2$ We simplify on the left side of the equation by adding: $41=c^2$ To solve the equation $41=c^2$, we must perform the opposite operation of squaring, which is taking the square root, in order to clear the exponent: $$41=c^2$$$$\sqrt {41}=\sqrt {c^2}$$$$c\approx\pm6.4$$$$c\approx6.4\text{ or }c\approx-6.4$$

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