Question
Answer
$$3\cdot\dfrac{\sqrt{3}}{5}\sqrt{75}=9$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3 \cdot \frac{\sqrt{3}}{5}\sqrt{75}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}3 \cdot \frac{\sqrt{3}}{5}\cdot5\sqrt{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{45}{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 45 : \color{orangered}{ 5 } }{ 5 : \color{orangered}{ 5 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{9}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}9\end{aligned} $$ | |
| ① | $$ \sqrt{75} =
\sqrt{ 5 ^2 \cdot 3 } =
\sqrt{ 5 ^2 } \, \sqrt{ 3 } =
5 \sqrt{ 3 }$$ |
| ② | $$ \color{blue}{ 3 \sqrt{3} } \cdot 5 \sqrt{3} = 45 $$$$ \color{blue}{ 5 } \cdot 1 = 5 $$ |
| ③ | Divide both the top and bottom numbers by $ \color{orangered}{ 5 } $. |
| ④ | Remove 1 from denominator. |
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