Question
Answer
$$\dfrac{\sqrt{450}}{10}=\dfrac{3\sqrt{2}}{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{450}}{10}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{ \sqrt{ 225 \cdot 2 } }{ 10 } \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{ \sqrt{ 225 } \cdot \sqrt{ 2 } }{ 10 } \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{15\sqrt{2}}{10} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 15 \cdot \sqrt{ 2 } : \color{orangered}{ 5 }}{ 10 : \color{orangered}{ 5 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{3\sqrt{2}}{2}\end{aligned} $$ | |
| ① | Factor out the largest perfect square of 450. ( in this example we factored out $ 225 $ ) |
| ② | Rewrite $ \sqrt{ 225 \cdot 2 } $ as the product of two radicals. |
| ③ | The square root of $ 225 $ is $ 15 $. |
| ④ | Divide numerator and denominator by $ \color{orangered}{ 5 } $. |
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