# How do you simplify (9sqrt 2)/( 6sqrt 18)?

Feb 1, 2016

Factor all the numbers as far as possible ($\sqrt{2}$ cannot be factored) and then cancel any terms which appear on top and bottom.

#### Explanation:

(9sqrt(2))/(6sqrt(18)

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

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

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

$= \frac{1}{2}$

Feb 1, 2016

$\frac{1}{2}$

#### Explanation:

first simplify $\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3 \sqrt{2}$

making use of : $\sqrt{a} \times \sqrt{b} = \sqrt{a} b \Leftrightarrow \sqrt{a} b = \sqrt{a} \times \sqrt{b}$

$\frac{9 \sqrt{2}}{6 \sqrt{18}} = \frac{9 \sqrt{2}}{6 \times 3 \sqrt{2}}$

$= \frac{9 \cancel{\sqrt{2}}}{18 \cancel{\sqrt{2}}} = \frac{9}{18} = \frac{1}{2}$