Question

State True or False

$\sqrt{a^3{b}^4}\sqrt[3]{3a^4{b}^3}$$=a^2{b}^3\cdot {\sqrt[6]{6a}}^5$

• A. True
• B. False

Answer 1

The correct option is A True

As given $\sqrt{a^3{b}^4}\sqrt[3]{3a^4{b}^3}$
$={\left(a^3\right)}^{\frac{1}{2}}{\left(b^4\right)}^{\frac{1}{2}}{\left(a^4\right)}^{\frac{1}{3}}{\left(b^3\right)}^{\frac{1}{3}}$
$=a^{\frac{3}{2}}{b}^2{a}^{\frac{4}{3}}b$
$=a^{\frac{3}{2}+\frac{4}{3}}{b}^{2+1}$
$=a^{\frac{17}{6}}{b}^3$
$=a^{\frac{12}{6}}{a}^{\frac{5}{6}}{b}^3$
$=a^2{b}^3{a}^{\frac{5}{6}}$
$=a^2{b}^3\cdot \sqrt[6]{6a^5}$