Question

State True or False.

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

• A. True
• B. False

Answer 1

The correct option is A True

As given $\sqrt{m^2{n}^2}\times \sqrt[6]{6m^2{n}^2}\times \sqrt[3]{3m^2{n}^2}$
$={\left(m^2\right)}^{\frac{1}{2}}{\left(n^2\right)}^{\frac{1}{2}}\times {\left(m^2\right)}^{\frac{1}{6}}{\left(n^2\right)}^{\frac{1}{6}}\times {\left(m^2\right)}^{\frac{1}{3}}{\left(n^2\right)}^{\frac{1}{3}}$
$=mn\times m^{\frac{1}{3}}{n}^{\frac{1}{3}}\times m^{\frac{2}{3}}{n}^{\frac{2}{3}}$
$=m^{1+\frac{1}{3}+\frac{2}{3}}\times n^{1+\frac{1}{3}+\frac{2}{3}}$
$=m^{\frac{6}{3}}{n}^{\frac{6}{3}}$
$=m^2{n}^2$