# How do you simplify sqrt(9/8)*sqrt(7/6)?

Apr 30, 2015

Simplify $\sqrt{\frac{9}{8}} \cdot \sqrt{\frac{7}{16}}$.

$\frac{\sqrt{9}}{\sqrt{8}} \cdot \frac{\sqrt{7}}{\sqrt{16}}$ =

$\frac{3}{\sqrt{2} \sqrt{4}} \cdot \frac{\sqrt{7}}{4}$ =

$\frac{3}{2 \sqrt{2}} \cdot \frac{\sqrt{7}}{4}$ =

$\frac{3 \sqrt{7}}{8 \sqrt{2}}$ =

Rationalize the denominator.

$\frac{3 \sqrt{7}}{8 \sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}$ =

$\frac{3 \sqrt{14}}{8 \sqrt{4}}$ =

$\frac{3 \sqrt{14}}{8 \cdot 2}$ =

$\frac{3 \sqrt{14}}{16}$