Express the following expression in simplest radical form. All variables represent positive real numbers. $\frac { \sqrt { 32 a ^ { 2 } b } } { \sqrt { 11 a ^ { 3 } b ^ { 3 } } }$
A) $\frac { 4 \sqrt { 22 } } { 11 a b ^ { 2 } }$
B) $\frac { 4 \sqrt { 22 a } } { b }$
C) $\frac { 4 \sqrt { 22 a } } { 11 a b }$
D) $\frac { 4 \sqrt { 22 a b } } { 11 b }$

Question

Quizplus · Accepted Answer

First, simplify the expression inside the radical and then divide: $\frac{\sqrt{32a^2b}}{\sqrt{11a^3b^3}} = \frac{\sqrt{32}}{\sqrt{11}} \cdot \frac{\sqrt{a^2}}{\sqrt{a^3}} \cdot \frac{\sqrt{b}}{\sqrt{b^3}} = \frac{4\sqrt{2}}{\sqrt{11}} \cdot \frac{a}{a\sqrt{a}} \cdot \frac{1}{b\sqrt{b}} = \frac{4\sqrt{22a}}{11ab}$.

Express the Following Expression in Simplest Radical Form 32a2b11a3b3\frac { \sqrt { 32 a ^ { 2 } b } } { \sqrt { 11 a ^ { 3 } b ^ { 3 } } }11a3b3​32a2b​​

Express the Following Expression in Simplest Radical Form $\frac { \sqrt { 32 a ^ { 2 } b } } { \sqrt { 11 a ^ { 3 } b ^ { 3 } } }$