Answer
$$\frac{1000}{\sqrt{2}}=500\sqrt{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{1000}{\sqrt{2}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 1000 }{\sqrt{ 2 }} \times \frac{ \color{orangered}{\sqrt{ 2 }} }{ \color{orangered}{\sqrt{ 2 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{1000\sqrt{2}}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 1000 \sqrt{ 2 } : \color{blue}{ 2 } }{ 2 : \color{blue}{ 2 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{500\sqrt{2}}{1} \xlongequal{ } \\[1 em] & \xlongequal{ }500\sqrt{2}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 2 }}$. |
| ② | In denominator we have $ \sqrt{ 2 } \cdot \sqrt{ 2 } = 2 $. |
| ③ | Divide both the top and bottom numbers by $ \color{blue}{ 2 }$. |
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