Answer
$$\frac{4\sqrt{243}}{4\sqrt{32}}=\frac{9\sqrt{6}}{8}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{4\sqrt{243}}{4\sqrt{32}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{4\sqrt{243}}{4\sqrt{32}}\frac{\sqrt{32}}{\sqrt{32}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{144\sqrt{6}}{128} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 144 \sqrt{ 6 } : \color{blue}{ 16 } } { 128 : \color{blue}{ 16 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{9\sqrt{6}}{8}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{32}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 4 \sqrt{243} } \cdot \sqrt{32} = 144 \sqrt{6} $$ Simplify denominator. $$ \color{blue}{ 4 \sqrt{32} } \cdot \sqrt{32} = 128 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 16 } $. |
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