Question
Answer
$$\dfrac{32}{\sqrt{40}}=\dfrac{8\sqrt{10}}{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{32}{\sqrt{40}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 32 }{\sqrt{ 40 }} \times \frac{ \color{orangered}{\sqrt{ 40 }} }{ \color{orangered}{\sqrt{ 40 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{32\sqrt{40}}{40} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 32 \sqrt{ 4 \cdot 10 }}{ 40 } \xlongequal{ } \\[1 em] & \xlongequal{ } \frac{ 32 \cdot 2 \sqrt{ 10 } }{ 40 } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{64\sqrt{10}}{40} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 64 \sqrt{ 10 } : \color{blue}{ 8 } }{ 40 : \color{blue}{ 8 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{8\sqrt{10}}{5}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 40 }}$. |
| ② | In denominator we have $ \sqrt{ 40 } \cdot \sqrt{ 40 } = 40 $. |
| ③ | Simplify $ \sqrt{ 40 } $. |
| ④ | Divide both the top and bottom numbers by $ \color{blue}{ 8 }$. |
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