Answer
$$\frac{8}{\sqrt{18}}=\frac{4\sqrt{2}}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{8}{\sqrt{18}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 8 }{\sqrt{ 18 }} \times \frac{ \color{orangered}{\sqrt{ 18 }} }{ \color{orangered}{\sqrt{ 18 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{8\sqrt{18}}{18} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 8 \sqrt{ 9 \cdot 2 }}{ 18 } \xlongequal{ } \\[1 em] & \xlongequal{ } \frac{ 8 \cdot 3 \sqrt{ 2 } }{ 18 } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{24\sqrt{2}}{18} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 24 \sqrt{ 2 } : \color{blue}{ 6 } }{ 18 : \color{blue}{ 6 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{4\sqrt{2}}{3}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 18 }}$. |
| ② | In denominator we have $ \sqrt{ 18 } \cdot \sqrt{ 18 } = 18 $. |
| ③ | Simplify $ \sqrt{ 18 } $. |
| ④ | Divide both the top and bottom numbers by $ \color{blue}{ 6 }$. |
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