Question
Answer
$$\dfrac{400}{\sqrt{300}}=\dfrac{40\sqrt{3}}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{400}{\sqrt{300}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 400 }{\sqrt{ 300 }} \times \frac{ \color{orangered}{\sqrt{ 300 }} }{ \color{orangered}{\sqrt{ 300 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{400\sqrt{300}}{300} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 400 \sqrt{ 100 \cdot 3 }}{ 300 } \xlongequal{ } \\[1 em] & \xlongequal{ } \frac{ 400 \cdot 10 \sqrt{ 3 } }{ 300 } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{4000\sqrt{3}}{300} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 4000 \sqrt{ 3 } : \color{blue}{ 100 } }{ 300 : \color{blue}{ 100 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{40\sqrt{3}}{3}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 300 }}$. |
| ② | In denominator we have $ \sqrt{ 300 } \cdot \sqrt{ 300 } = 300 $. |
| ③ | Simplify $ \sqrt{ 300 } $. |
| ④ | Divide both the top and bottom numbers by $ \color{blue}{ 100 }$. |
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