# Chapter 8 - Section 8.4 - Rationalizing the Denominator - Exercise Set: 27

$\frac{3\sqrt2}{2}$

#### Work Step by Step

$\frac{12}{\sqrt{32}}$ Simplify by factoring out perfect squares. $\frac{12}{\sqrt{(16)(2)}}$ Simplify. $\frac{12}{4\sqrt2}$ Rationalize the denominator. $\frac{12}{4\sqrt2}\times\frac{\sqrt2}{\sqrt2}$ Use product rule for square roots. $\frac{12\sqrt{2}}{8}$ Reduce. Divide the numerator and denominator by greatest common factor of 4. $\frac{3\sqrt2}{2}$

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