Question

simplify. assume all variables are positive.
\sqrt{2r^{6}s^{5}} \cdot \sqrt{6r^{8}s^{7}}

\sqrt{2r^{6}s^{5}} \cdot \sqrt{6r^{8}s^{7}} = \square
(type an exact answer, using radicals as needed.)

Explanation:

Step1: Combine radicals into one

$\sqrt{2r^6s^5 \cdot 6r^8s^7}$

Step2: Multiply coefficients and variables

$\sqrt{(2 \cdot 6) \cdot r^{6+8} \cdot s^{5+7}}$
$\sqrt{12r^{14}s^{12}}$

Step3: Split radical into separate terms

$\sqrt{12} \cdot \sqrt{r^{14}} \cdot \sqrt{s^{12}}$

Step4: Simplify each radical

$\sqrt{4 \cdot 3} \cdot r^{7} \cdot s^{6}$
$2\sqrt{3}r^7s^6$

Answer:

$2\sqrt{3}r^7s^6$