Question

simplify. assume all variables are positive.
\sqrt{2r^{4}s^{5}} \cdot \sqrt{6r^{8}s^{3}}

\sqrt{2r^{4}s^{5}} \cdot \sqrt{6r^{8}s^{3}} = \square
(type an exact answer, using radicals as needed.)

Explanation:

Step1: Combine square roots

$\sqrt{2r^4s^5} \cdot \sqrt{6r^8s^3} = \sqrt{(2r^4s^5)(6r^8s^3)}$

Step2: Multiply coefficients & variables

$\sqrt{2 \cdot 6 \cdot r^{4+8} \cdot s^{5+3}} = \sqrt{12r^{12}s^8}$

Step3: Simplify the radical

$\sqrt{4 \cdot 3 \cdot r^{12} \cdot s^8} = \sqrt{4} \cdot \sqrt{3} \cdot \sqrt{r^{12}} \cdot \sqrt{s^8}$
$\sqrt{4}=2$, $\sqrt{r^{12}}=r^6$, $\sqrt{s^8}=s^4$
$=2r^6s^4\sqrt{3}$

Answer:

$2r^6s^4\sqrt{3}$