Question

simplify. assume all variables are positive.\\(sqrt{2r^{2}s^{5}} cdot sqrt{14r^{4}s^{9}}\\)\\(sqrt{2r^{2}s^{5}} cdot sqrt{14r^{4}s^{9}} = square\\)(type an exact answer, using radicals as needed.)

Explanation:

Step1: Combine radicals into one

$\sqrt{2r^2s^5 \cdot 14r^4s^9}$

Step2: Multiply coefficients and like variables

$\sqrt{(2 \cdot 14)r^{2+4}s^{5+9}} = \sqrt{28r^6s^{14}}$

Step3: Factor into perfect squares

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

Step4: Simplify perfect square radicals

$\sqrt{4} \cdot \sqrt{(r^3)^2} \cdot \sqrt{(s^7)^2} \cdot \sqrt{7} = 2r^3s^7\sqrt{7}$

Answer:

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