How do you simplify (sqrt9sqrt8)/(sqrt6sqrt6)?

Mar 30, 2017

Answer:

$\sqrt{2}$

Explanation:

$\frac{\sqrt{9} \sqrt{8}}{\sqrt{6} \sqrt{6}} = \frac{3 \cdot \sqrt{2 \cdot 4}}{6}$

$= \frac{3 \cdot 2 \sqrt{2}}{6} = \frac{6 \sqrt{2}}{6}$

$= \sqrt{2}$

Mar 30, 2017

There are different methods which can be used:

First option: Combine the radicals:

$\frac{\sqrt{9} \sqrt{8}}{\sqrt{6} \sqrt{6}} = \frac{\sqrt{72}}{\sqrt{36}} = \sqrt{\frac{72}{36}} = \sqrt{2}$

Second option: Simplify where possible, find factors of radicands.

$\frac{\textcolor{red}{\sqrt{9}} \textcolor{b l u e}{\sqrt{8}}}{\textcolor{g r e e n}{\sqrt{6} \sqrt{6}}}$

$= \frac{\textcolor{red}{3} \textcolor{b l u e}{\sqrt{4 \times 2}}}{{\textcolor{g r e e n}{\sqrt{6}}}^{2}}$

=(color(red)(3)color(blue)(xx2sqrt(2)))/(color(green)(6)

$= \sqrt{2}$

Third option: Write as the product of prime factors:

$\frac{\sqrt{9} \sqrt{8}}{\sqrt{6} \sqrt{6}}$

$= \frac{\sqrt{3} \times \sqrt{3} \times \sqrt{2} \times \sqrt{2} \times \sqrt{2}}{\sqrt{2} \times \sqrt{3} \times \sqrt{2} \times \sqrt{3}} \text{ }$ now cancel

$= \frac{\cancel{\sqrt{3}} \times \cancel{\sqrt{3}} \times \cancel{\sqrt{2}} \times \cancel{\sqrt{2}} \times \sqrt{2}}{\cancel{\sqrt{2}} \times \cancel{\sqrt{3}} \times \cancel{\sqrt{2}} \times \cancel{\sqrt{3}}}$

$= \sqrt{2}$