Question
Answer
$$\dfrac{3\sqrt{5}\cdot4\sqrt{2}}{3\sqrt{40}}=2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{3\sqrt{5}\cdot4\sqrt{2}}{3\sqrt{40}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{3\sqrt{5}\cdot4\sqrt{2}}{3\sqrt{40}}\frac{\sqrt{40}}{\sqrt{40}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{240}{120} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 240 : \color{orangered}{ 120 } }{ 120 : \color{orangered}{ 120 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{2}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{40}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 12 \sqrt{10} } \cdot \sqrt{40} = 240 $$ Simplify denominator. $$ \color{blue}{ 3 \sqrt{40} } \cdot \sqrt{40} = 120 $$ |
| ③ | Divide both the top and bottom numbers by $ \color{orangered}{ 120 } $. |
| ④ | Remove 1 from denominator. |
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