Question
Answer
$$\dfrac{24}{\sqrt{147}}=\dfrac{8\sqrt{3}}{7}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{24}{\sqrt{147}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 24 }{\sqrt{ 147 }} \times \frac{ \color{orangered}{\sqrt{ 147 }} }{ \color{orangered}{\sqrt{ 147 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{24\sqrt{147}}{147} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 24 \sqrt{ 49 \cdot 3 }}{ 147 } \xlongequal{ } \\[1 em] & \xlongequal{ } \frac{ 24 \cdot 7 \sqrt{ 3 } }{ 147 } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{168\sqrt{3}}{147} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 168 \sqrt{ 3 } : \color{blue}{ 21 } }{ 147 : \color{blue}{ 21 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{8\sqrt{3}}{7}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 147 }}$. |
| ② | In denominator we have $ \sqrt{ 147 } \cdot \sqrt{ 147 } = 147 $. |
| ③ | Simplify $ \sqrt{ 147 } $. |
| ④ | Divide both the top and bottom numbers by $ \color{blue}{ 21 }$. |
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