Question
Answer
$$\dfrac{11}{\sqrt{1331}}=\dfrac{\sqrt{11}}{11}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{11}{\sqrt{1331}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 11 }{\sqrt{ 1331 }} \times \frac{ \color{orangered}{\sqrt{ 1331 }} }{ \color{orangered}{\sqrt{ 1331 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{11\sqrt{1331}}{1331} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 11 \sqrt{ 121 \cdot 11 }}{ 1331 } \xlongequal{ } \\[1 em] & \xlongequal{ } \frac{ 11 \cdot 11 \sqrt{ 11 } }{ 1331 } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{121\sqrt{11}}{1331} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 121 \sqrt{ 11 } : \color{blue}{ 121 } }{ 1331 : \color{blue}{ 121 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{\sqrt{11}}{11}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 1331 }}$. |
| ② | In denominator we have $ \sqrt{ 1331 } \cdot \sqrt{ 1331 } = 1331 $. |
| ③ | Simplify $ \sqrt{ 1331 } $. |
| ④ | Divide both the top and bottom numbers by $ \color{blue}{ 121 }$. |
This page was created using
Rationalize Denominator Calculator