# How do you simplify sqrt(1215)?

Feb 22, 2016

$9 \sqrt{15}$

#### Explanation:

First decompose 1215 in prime factors:

The last digit is 5 so it is multiple o f5:

$\frac{1215}{5} = 243$

The sum of the digits of 243 its is 9, therefore it is multiple 3.

$\frac{243}{3} = 81$.

We know by the grammar school that $81 = 9 \times 9 = {3}^{4}$.

So $1215 = {3}^{5} \cdot 5$

$S q r t \left(1215\right) = \sqrt{{3}^{5} \cdot 5} = \sqrt{{3}^{4} \cdot 3 \cdot 5} = {3}^{2} \sqrt{3 \cdot 5} = 9 \sqrt{15}$