Answer
$$\frac{3\sqrt{82}\cdot3\sqrt{12}}{3\sqrt{48}}=\frac{3\sqrt{82}}{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{3\sqrt{82}\cdot3\sqrt{12}}{3\sqrt{48}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{3\sqrt{82}\cdot3\sqrt{12}}{3\sqrt{48}}\frac{\sqrt{48}}{\sqrt{48}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{216\sqrt{82}}{144} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 216 \sqrt{ 82 } : \color{blue}{ 72 } } { 144 : \color{blue}{ 72 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{3\sqrt{82}}{2}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{48}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 9 \sqrt{984} } \cdot \sqrt{48} = 216 \sqrt{82} $$ Simplify denominator. $$ \color{blue}{ 3 \sqrt{48} } \cdot \sqrt{48} = 144 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 72 } $. |
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