Question

simplify. assume all variables are positive.
\sqrt{3r^{8}s^{9}} \cdot \sqrt{6r^{2}s^{7}}
\sqrt{3r^{8}s^{9}} \cdot \sqrt{6r^{2}s^{7}} = \square
(type an exact answer, using radicals as needed.)

Explanation:

Step1: Combine the square roots

$\sqrt{3r^8s^9} \cdot \sqrt{6r^2s^7} = \sqrt{(3r^8s^9)(6r^2s^7)}$

Step2: Multiply coefficients and like variables

$\sqrt{3 \cdot 6 \cdot r^{8+2} \cdot s^{9+7}} = \sqrt{18r^{10}s^{16}}$

Step3: Factor into perfect squares

$\sqrt{9 \cdot 2 \cdot r^{10} \cdot s^{16}} = \sqrt{9} \cdot \sqrt{2} \cdot \sqrt{r^{10}} \cdot \sqrt{s^{16}}$

Step4: Simplify each perfect square

$3 \cdot \sqrt{2} \cdot r^{5} \cdot s^{8}$

Step5: Rearrange into standard form

$3r^5s^8\sqrt{2}$

Answer:

$3r^5s^8\sqrt{2}$