Question
Answer
$$\dfrac{-27}{\sqrt{748}}=-\dfrac{27\sqrt{187}}{374}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{-27}{\sqrt{748}}& \xlongequal{ }-\frac{27}{\sqrt{748}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}- \, \frac{ 27 }{\sqrt{ 748 }} \times \frac{ \color{orangered}{\sqrt{ 748 }} }{ \color{orangered}{\sqrt{ 748 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-\frac{27\sqrt{748}}{748} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}- \, \frac{ 27 \sqrt{ 4 \cdot 187 }}{ 748 } \xlongequal{ } \\[1 em] & \xlongequal{ }- \, \frac{ 27 \cdot 2 \sqrt{ 187 } }{ 748 } \xlongequal{ } \\[1 em] & \xlongequal{ }-\frac{54\sqrt{187}}{748} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}- \, \frac{ 54 \sqrt{ 187 } : \color{blue}{ 2 } }{ 748 : \color{blue}{ 2 } } \xlongequal{ } \\[1 em] & \xlongequal{ }-\frac{27\sqrt{187}}{374}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 748 }}$. |
| ② | In denominator we have $ \sqrt{ 748 } \cdot \sqrt{ 748 } = 748 $. |
| ③ | Simplify $ \sqrt{ 748 } $. |
| ④ | Divide both the top and bottom numbers by $ \color{blue}{ 2 }$. |
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