Question
Answer
$$\dfrac{5}{\sqrt{99}}=\dfrac{5\sqrt{11}}{33}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{5}{\sqrt{99}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 5 }{\sqrt{ 99 }} \times \frac{ \color{orangered}{\sqrt{ 99 }} }{ \color{orangered}{\sqrt{ 99 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{5\sqrt{99}}{99} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 5 \sqrt{ 9 \cdot 11 }}{ 99 } \xlongequal{ } \\[1 em] & \xlongequal{ } \frac{ 5 \cdot 3 \sqrt{ 11 } }{ 99 } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{15\sqrt{11}}{99} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 15 \sqrt{ 11 } : \color{blue}{ 3 } }{ 99 : \color{blue}{ 3 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{5\sqrt{11}}{33}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 99 }}$. |
| ② | In denominator we have $ \sqrt{ 99 } \cdot \sqrt{ 99 } = 99 $. |
| ③ | Simplify $ \sqrt{ 99 } $. |
| ④ | Divide both the top and bottom numbers by $ \color{blue}{ 3 }$. |
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