Question
Answer
$$\dfrac{\sqrt{200}}{28}=\dfrac{5\sqrt{2}}{14}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{200}}{28}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{ \sqrt{ 100 \cdot 2 } }{ 28 } \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{ \sqrt{ 100 } \cdot \sqrt{ 2 } }{ 28 } \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{10\sqrt{2}}{28} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 10 \cdot \sqrt{ 2 } : \color{orangered}{ 2 }}{ 28 : \color{orangered}{ 2 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{5\sqrt{2}}{14}\end{aligned} $$ | |
| ① | Factor out the largest perfect square of 200. ( in this example we factored out $ 100 $ ) |
| ② | Rewrite $ \sqrt{ 100 \cdot 2 } $ as the product of two radicals. |
| ③ | The square root of $ 100 $ is $ 10 $. |
| ④ | Divide numerator and denominator by $ \color{orangered}{ 2 } $. |
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