# What is the square root of 16.2?

Sep 9, 2015

$\sqrt{16.2} = \frac{9 \sqrt{5}}{5} \approx 4.0249$
Use: $\sqrt{a b} = \sqrt{a} \sqrt{b}$ if $a , b \ge 0$
and: $\sqrt{{a}^{2}} = a$ if $a \ge 0$
$\sqrt{16.2} = \sqrt{\frac{81}{5}} = \sqrt{\frac{{9}^{2} \cdot 5}{{5}^{2}}} = \sqrt{{9}^{2} / {5}^{2}} \sqrt{5} = \frac{9 \sqrt{5}}{5} \approx 4.0249$