Question
Answer
$$\dfrac{5}{\sqrt{68}}=\dfrac{5\sqrt{17}}{34}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{5}{\sqrt{68}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 5 }{\sqrt{ 68 }} \times \frac{ \color{orangered}{\sqrt{ 68 }} }{ \color{orangered}{\sqrt{ 68 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{5\sqrt{68}}{68} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 5 \sqrt{ 4 \cdot 17 }}{ 68 } \xlongequal{ } \\[1 em] & \xlongequal{ } \frac{ 5 \cdot 2 \sqrt{ 17 } }{ 68 } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{10\sqrt{17}}{68} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 10 \sqrt{ 17 } : \color{blue}{ 2 } }{ 68 : \color{blue}{ 2 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{5\sqrt{17}}{34}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 68 }}$. |
| ② | In denominator we have $ \sqrt{ 68 } \cdot \sqrt{ 68 } = 68 $. |
| ③ | Simplify $ \sqrt{ 68 } $. |
| ④ | Divide both the top and bottom numbers by $ \color{blue}{ 2 }$. |
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