Question
Answer
$$\dfrac{9}{\sqrt{162}}=\dfrac{\sqrt{2}}{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{9}{\sqrt{162}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 9 }{\sqrt{ 162 }} \times \frac{ \color{orangered}{\sqrt{ 162 }} }{ \color{orangered}{\sqrt{ 162 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{9\sqrt{162}}{162} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 9 \sqrt{ 81 \cdot 2 }}{ 162 } \xlongequal{ } \\[1 em] & \xlongequal{ } \frac{ 9 \cdot 9 \sqrt{ 2 } }{ 162 } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{81\sqrt{2}}{162} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 81 \sqrt{ 2 } : \color{blue}{ 81 } }{ 162 : \color{blue}{ 81 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{\sqrt{2}}{2}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 162 }}$. |
| ② | In denominator we have $ \sqrt{ 162 } \cdot \sqrt{ 162 } = 162 $. |
| ③ | Simplify $ \sqrt{ 162 } $. |
| ④ | Divide both the top and bottom numbers by $ \color{blue}{ 81 }$. |
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