Question
Answer
$$\dfrac{1}{\sqrt{180}}=\dfrac{\sqrt{5}}{30}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{1}{\sqrt{180}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 1 }{\sqrt{ 180 }} \times \frac{ \color{orangered}{\sqrt{ 180 }} }{ \color{orangered}{\sqrt{ 180 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{1\sqrt{180}}{180} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{\sqrt{180}}{180} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{\sqrt{ 36 \cdot 5 }}{ 180 } \xlongequal{ } \\[1 em] & \xlongequal{ } \frac{\sqrt{ 36 } \cdot \sqrt{ 5 }}{ 180 } \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{6\sqrt{5}}{180} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}} \frac{ 6 \sqrt{ 5 } : \color{blue}{ 6 } }{ 180 : \color{blue}{ 6 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{\sqrt{5}}{30}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 180 }}$. |
| ② | In denominator we have $ \sqrt{ 180 } \cdot \sqrt{ 180 } = 180 $. |
| ③ | Simplify $ \sqrt{ 180 } $. |
| ④ | The square root of $ 36 $ is $ 6 $. |
| ⑤ | Divide both the top and bottom numbers by $ \color{blue}{ 6 }$. |
This page was created using
Rationalize Denominator Calculator