Question

simplify. assume all variables are positive.
\sqrt{3r^{8}s^{5}} \cdot \sqrt{15r^{4}s^{9}}
\sqrt{3r^{8}s^{5}} \cdot \sqrt{15r^{4}s^{9}} = \square
(type an exact answer, using radicals as needed.)

Explanation:

Step1: Combine radicals into one

$\sqrt{3r^8s^5 \cdot 15r^4s^9}$

Step2: Multiply coefficients and like variables

$\sqrt{(3 \cdot 15)r^{8+4}s^{5+9}} = \sqrt{45r^{12}s^{14}}$

Step3: Factor into perfect squares

$\sqrt{9 \cdot 5 \cdot (r^6)^2 \cdot (s^7)^2}$

Step4: Extract perfect square factors

$\sqrt{9} \cdot \sqrt{(r^6)^2} \cdot \sqrt{(s^7)^2} \cdot \sqrt{5} = 3r^6s^7\sqrt{5}$

Answer:

$3r^6s^7\sqrt{5}$