# How do you rationalize the denominator and simplify sqrt18/sqrt3?

May 14, 2016

$18 = 3 \cdot 3 \cdot 2 = {3}^{2} \cdot 2$

$\frac{\sqrt{18}}{\sqrt{3}}$

$\frac{\sqrt{{3}^{2} \cdot 2}}{\sqrt{3}}$

$\frac{\sqrt{{3}^{2}} \cdot \sqrt{2}}{\sqrt{3}}$

$\frac{3 \cdot \sqrt{2}}{\sqrt{3}}$

$\frac{3 \cdot \sqrt{2}}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}$

$\frac{3 \cdot \sqrt{2} \cdot \sqrt{3}}{3}$

$\frac{\cancel{3} \cdot \sqrt{2} \cdot \sqrt{3}}{\cancel{3}}$

$\sqrt{2 \cdot 3}$