# How do you simplify sqrt(2205)?

Jan 25, 2016

$21 \sqrt{5}$

#### Explanation:

The key to this solution is to represent $2205$ as a product of some numbers that are squares of some other numbers and to use a property of square roots that allows to do the following for any two non-negative real numbers $X$ and $Y$:
$\sqrt{X \cdot Y} = \sqrt{X} \cdot \sqrt{Y}$

Using this, we can perform the following steps:
$\sqrt{2205} = \sqrt{9 \cdot 245} =$
$= \sqrt{9} \cdot \sqrt{245} =$
$= \sqrt{9} \cdot \sqrt{49 \cdot 5} =$
$= \sqrt{9} \cdot \sqrt{49} \cdot \sqrt{5} =$
$= 3 \cdot 7 \cdot \sqrt{5} = 21 \sqrt{5}$