# Question #61863

Jan 15, 2017

$- 31 \sqrt{2}$.

#### Explanation:

Although not immediately apparent, this expression can be simplified.

Using the property that $\sqrt{a b} = \sqrt{a} \sqrt{b}$, we can rewrite as:

$3 \sqrt{18} - 8 \sqrt{50} = 3 \sqrt{9 \cdot 2} - 8 \sqrt{25 \cdot 2} = 3 \sqrt{9} \sqrt{2} - 8 \sqrt{25} \sqrt{2}$.

Since $\sqrt{9} = 3$ and $\sqrt{25} = 5$, this is:

$9 \sqrt{2} - 40 \sqrt{2} = - 31 \sqrt{2}$.