Question
Answer
$$\dfrac{\sqrt{2}^4}{\sqrt{2}}\cdot5=10\sqrt{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{2}^4}{\sqrt{2}}\cdot5& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{4}{\sqrt{2}}\cdot5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{ 4 }{\sqrt{ 2 }} \times \frac{ \color{orangered}{\sqrt{ 2 }} }{ \color{orangered}{\sqrt{ 2 }}} \cdot 5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{4\sqrt{2}}{2}\cdot5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{ 4 \sqrt{ 2 } : \color{blue}{ 2 } }{ 2 : \color{blue}{ 2 } } \cdot 5 \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{2\sqrt{2}}{1}\cdot5 \xlongequal{ } \\[1 em] & \xlongequal{ }2\sqrt{2}\cdot5 \xlongequal{ } \\[1 em] & \xlongequal{ }2\cdot5\sqrt{2} \xlongequal{ } \\[1 em] & \xlongequal{ }10\sqrt{2}\end{aligned} $$ | |
| ① | $$ \sqrt{2}^4 =
\left( \sqrt{2} ^2 \right)^{ 2 } =
\lvert 2 \rvert ^{ 2 } =
4 $$ |
| ② | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 2 }}$. |
| ③ | In denominator we have $ \sqrt{ 2 } \cdot \sqrt{ 2 } = 2 $. |
| ④ | Divide both the top and bottom numbers by $ \color{blue}{ 2 }$. |
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