Question
Answer
$$\dfrac{5}{\sqrt{343}}=\dfrac{5\sqrt{7}}{49}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{5}{\sqrt{343}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 5 }{\sqrt{ 343 }} \times \frac{ \color{orangered}{\sqrt{ 343 }} }{ \color{orangered}{\sqrt{ 343 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{5\sqrt{343}}{343} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 5 \sqrt{ 49 \cdot 7 }}{ 343 } \xlongequal{ } \\[1 em] & \xlongequal{ } \frac{ 5 \cdot 7 \sqrt{ 7 } }{ 343 } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{35\sqrt{7}}{343} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 35 \sqrt{ 7 } : \color{blue}{ 7 } }{ 343 : \color{blue}{ 7 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{5\sqrt{7}}{49}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 343 }}$. |
| ② | In denominator we have $ \sqrt{ 343 } \cdot \sqrt{ 343 } = 343 $. |
| ③ | Simplify $ \sqrt{ 343 } $. |
| ④ | Divide both the top and bottom numbers by $ \color{blue}{ 7 }$. |
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