Question
Answer
$$\dfrac{2\sqrt{45}}{1}=6\sqrt{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2\sqrt{45}}{1}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2\sqrt{45} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2\cdot \sqrt{ 9 \cdot 5 } \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2\cdot \sqrt{ 9 } \cdot \sqrt{ 5 } \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2\cdot3 \sqrt{ 5 } \xlongequal{ } \\[1 em] & \xlongequal{ }6\sqrt{5}\end{aligned} $$ | |
| ① | Remove 1 from denominator. |
| ② | Factor out the largest perfect square of 45. ( in this example we factored out $ 9 $ ) |
| ③ | Rewrite $ \sqrt{ 9 \cdot 5 } $ as the product of two radicals. |
| ④ | The square root of $ 9 $ is $ 3 $. |
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