Question

simplify. assume all variables are positive.
\sqrt{2r^{4}s^{5}}\cdot\sqrt{10r^{6}s^{7}}
\sqrt{2r^{4}s^{5}}\cdot\sqrt{10r^{6}s^{7}} = \square
(type an exact answer, using radicals as needed.)

Explanation:

Step1: Combine radicals into one

$\sqrt{2r^4s^5 \cdot 10r^6s^7}$

Step2: Multiply coefficients and like variables

$\sqrt{(2 \cdot 10) \cdot r^{4+6} \cdot s^{5+7}} = \sqrt{20r^{10}s^{12}}$

Step3: Factor into perfect squares

$\sqrt{4 \cdot 5 \cdot r^{10} \cdot s^{12}} = \sqrt{4} \cdot \sqrt{5} \cdot \sqrt{r^{10}} \cdot \sqrt{s^{12}}$

Step4: Simplify each perfect square

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

Step5: Rearrange terms

$2r^5s^6\sqrt{5}$

Answer:

$2r^5s^6\sqrt{5}$