Question

1. simplify the expression below.

\sqrt3{81m^{8}n^{4}}
a. \\ 9m^{2}n\sqrt3{n}
b. \\ 9m^{3}n\sqrt3{m^{2}n}
c. \\ 3m^{2}n\sqrt3{3n}
d. \\ 3m^{2}n\sqrt3{3m^{2}n}

Explanation:

Step1: Factor the radicand

$\sqrt[3]{81m^8n^4} = \sqrt[3]{27 \times 3 \times m^6 \times m^2 \times n^3 \times n}$

Step2: Separate perfect cubes

$\sqrt[3]{27m^6n^3} \times \sqrt[3]{3m^2n}$

Step3: Simplify perfect cube roots

$3m^2n \times \sqrt[3]{3m^2n}$

Answer:

D. $3m^2n\sqrt[3]{3m^2n}$