Question

Simplify and express the result in its simplest form

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

• A. $m^2{n}^2$
• B. $m^{2}n$
• C. $m^3{n}^3$
• D. $m{n}^2$

Answer 1

The correct option is A $m^2{n}^2$

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

$=m^{\frac{2}{2}+\frac{2}{6}+\frac{2}{3}}\times n^{\frac{2}{2}+\frac{2}{6}+\frac{2}{3}}$

$=m^{\frac{6+2+4}{6}}\times n^{\frac{6+2+4}{6}}$

$=m^2{n}^2$