# Chapter 7 - Section 7.3 - Simplifying Radicals, the Distance Formula, and Circles - 7.3 Exercises: 116

$b=3\sqrt 5$

#### Work Step by Step

According to the Pythagorean Theorem, if $a$ and $b$ are the lengths of the shorter sides of a right triangle and $c$ is the length of the longest side, then $a^{2}+b^{2}=c^{2}$. Therefore, $6^{2}+b^{2}=9^{2}$. $36+b^{2}=81$ Subtract 36 from both sides. $b^{2}=45$ Take the square root of both sides. $b=\sqrt 45=\sqrt (9\times5)=\sqrt 9\times\sqrt5=3\sqrt 5$

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