Question
Answer
$$-\dfrac{11}{\sqrt{112}}=-\dfrac{11\sqrt{7}}{28}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-\frac{11}{\sqrt{112}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}- \, \frac{ 11 }{\sqrt{ 112 }} \times \frac{ \color{orangered}{\sqrt{ 112 }} }{ \color{orangered}{\sqrt{ 112 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-\frac{11\sqrt{112}}{112} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}- \, \frac{ 11 \sqrt{ 16 \cdot 7 }}{ 112 } \xlongequal{ } \\[1 em] & \xlongequal{ }- \, \frac{ 11 \cdot 4 \sqrt{ 7 } }{ 112 } \xlongequal{ } \\[1 em] & \xlongequal{ }-\frac{44\sqrt{7}}{112} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}- \, \frac{ 44 \sqrt{ 7 } : \color{blue}{ 4 } }{ 112 : \color{blue}{ 4 } } \xlongequal{ } \\[1 em] & \xlongequal{ }-\frac{11\sqrt{7}}{28}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 112 }}$. |
| ② | In denominator we have $ \sqrt{ 112 } \cdot \sqrt{ 112 } = 112 $. |
| ③ | Simplify $ \sqrt{ 112 } $. |
| ④ | Divide both the top and bottom numbers by $ \color{blue}{ 4 }$. |
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