Question
Answer
$$\dfrac{3}{\sqrt{594}}=\dfrac{\sqrt{66}}{66}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{3}{\sqrt{594}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 3 }{\sqrt{ 594 }} \times \frac{ \color{orangered}{\sqrt{ 594 }} }{ \color{orangered}{\sqrt{ 594 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{3\sqrt{594}}{594} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 3 \sqrt{ 9 \cdot 66 }}{ 594 } \xlongequal{ } \\[1 em] & \xlongequal{ } \frac{ 3 \cdot 3 \sqrt{ 66 } }{ 594 } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{9\sqrt{66}}{594} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 9 \sqrt{ 66 } : \color{blue}{ 9 } }{ 594 : \color{blue}{ 9 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{\sqrt{66}}{66}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 594 }}$. |
| ② | In denominator we have $ \sqrt{ 594 } \cdot \sqrt{ 594 } = 594 $. |
| ③ | Simplify $ \sqrt{ 594 } $. |
| ④ | Divide both the top and bottom numbers by $ \color{blue}{ 9 }$. |
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