Question
Answer
$$\dfrac{69}{\sqrt{342}}=\dfrac{23\sqrt{38}}{38}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{69}{\sqrt{342}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 69 }{\sqrt{ 342 }} \times \frac{ \color{orangered}{\sqrt{ 342 }} }{ \color{orangered}{\sqrt{ 342 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{69\sqrt{342}}{342} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 69 \sqrt{ 9 \cdot 38 }}{ 342 } \xlongequal{ } \\[1 em] & \xlongequal{ } \frac{ 69 \cdot 3 \sqrt{ 38 } }{ 342 } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{207\sqrt{38}}{342} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 207 \sqrt{ 38 } : \color{blue}{ 9 } }{ 342 : \color{blue}{ 9 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{23\sqrt{38}}{38}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 342 }}$. |
| ② | In denominator we have $ \sqrt{ 342 } \cdot \sqrt{ 342 } = 342 $. |
| ③ | Simplify $ \sqrt{ 342 } $. |
| ④ | Divide both the top and bottom numbers by $ \color{blue}{ 9 }$. |
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