Question
Answer
$$\dfrac{27}{\sqrt{243}}=\sqrt{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{27}{\sqrt{243}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 27 }{\sqrt{ 243 }} \times \frac{ \color{orangered}{\sqrt{ 243 }} }{ \color{orangered}{\sqrt{ 243 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{27\sqrt{243}}{243} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 27 \sqrt{ 81 \cdot 3 }}{ 243 } \xlongequal{ } \\[1 em] & \xlongequal{ } \frac{ 27 \cdot 9 \sqrt{ 3 } }{ 243 } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{243\sqrt{3}}{243} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 243 \sqrt{ 3 } : \color{blue}{ 243 } }{ 243 : \color{blue}{ 243 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{\sqrt{3}}{1} \xlongequal{ } \\[1 em] & \xlongequal{ }\sqrt{3}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 243 }}$. |
| ② | In denominator we have $ \sqrt{ 243 } \cdot \sqrt{ 243 } = 243 $. |
| ③ | Simplify $ \sqrt{ 243 } $. |
| ④ | Divide both the top and bottom numbers by $ \color{blue}{ 243 }$. |
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