Question

simplify assume all variables are positive.
\sqrt{3r^{6}s^{3}} \cdot \sqrt{33r^{2}s^{5}}
\sqrt{3r^{6}s^{3}} \cdot \sqrt{33r^{2}s^{5}} = \square
(type an exact answer, using radicals as needed.)

Explanation:

Step1: Combine square roots

$\sqrt{3r^6s^3} \cdot \sqrt{33r^2s^5} = \sqrt{3r^6s^3 \cdot 33r^2s^5}$

Step2: Multiply coefficients & variables

$\sqrt{(3 \cdot 33) \cdot (r^6 \cdot r^2) \cdot (s^3 \cdot s^5)} = \sqrt{99r^8s^8}$

Step3: Factor perfect squares

$\sqrt{9 \cdot 11 \cdot r^8 \cdot s^8} = \sqrt{9} \cdot \sqrt{r^8} \cdot \sqrt{s^8} \cdot \sqrt{11}$

Step4: Simplify perfect square roots

$\sqrt{9}=3$, $\sqrt{r^8}=r^4$, $\sqrt{s^8}=s^4$

Answer:

$3r^4s^4\sqrt{11}$