Question

algebra ii - s2 / module 8 / lesson 110

1. simplify.

$sqrt{8mn} cdot sqrt{3m^3n}$
$\bigcirc$ $2m^2nsqrt{6}$
$\bigcirc$ $6m^2nsqrt{2}$
$\bigcirc$ $4mn^2sqrt{6}$
$\bigcirc$ $2m^2sqrt{6n}$

Explanation:

Step1: Combine square roots

$\sqrt{8mn} \cdot \sqrt{3m^3n} = \sqrt{8mn \cdot 3m^3n}$

Step2: Multiply inside the root

$\sqrt{24m^{1+3}n^{1+1}} = \sqrt{24m^4n^2}$

Step3: Simplify the radical

$\sqrt{4 \cdot 6 \cdot m^4 \cdot n^2} = \sqrt{4} \cdot \sqrt{m^4} \cdot \sqrt{n^2} \cdot \sqrt{6} = 2m^2n\sqrt{6}$

Answer:

A. $2m^2n\sqrt{6}$