Answer
$$\frac{21}{\sqrt{135}}=\frac{7\sqrt{15}}{15}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{21}{\sqrt{135}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 21 }{\sqrt{ 135 }} \times \frac{ \color{orangered}{\sqrt{ 135 }} }{ \color{orangered}{\sqrt{ 135 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{21\sqrt{135}}{135} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 21 \sqrt{ 9 \cdot 15 }}{ 135 } \xlongequal{ } \\[1 em] & \xlongequal{ } \frac{ 21 \cdot 3 \sqrt{ 15 } }{ 135 } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{63\sqrt{15}}{135} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 63 \sqrt{ 15 } : \color{blue}{ 9 } }{ 135 : \color{blue}{ 9 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{7\sqrt{15}}{15}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 135 }}$. |
| ② | In denominator we have $ \sqrt{ 135 } \cdot \sqrt{ 135 } = 135 $. |
| ③ | Simplify $ \sqrt{ 135 } $. |
| ④ | Divide both the top and bottom numbers by $ \color{blue}{ 9 }$. |
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