# How do you find the square root of 189?

Jul 19, 2015

$\sqrt{189} = \sqrt{{3}^{2} \cdot 21} = 3 \sqrt{21}$

#### Explanation:

If $a , b \ge 0$ then $\sqrt{a b} = \sqrt{a} \sqrt{b}$

So:

$\sqrt{189} = \sqrt{9 \cdot 21} = \sqrt{{3}^{2} \cdot 21} = \sqrt{{3}^{2}} \sqrt{21} = 3 \sqrt{21}$

This cannot be simplified further since $21$ has no square factors larger than $1$