Question
Answer
$$8\cdot\dfrac{\sqrt{27}}{2}\sqrt{45}=36\sqrt{15}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}8 \cdot \frac{\sqrt{27}}{2}\sqrt{45}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}8 \cdot \frac{\sqrt{27}}{2}\cdot3\sqrt{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}8 \cdot \frac{3\sqrt{3}}{2}\cdot3\sqrt{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{72\sqrt{15}}{2} \xlongequal{ } \\[1 em] & \xlongequal{ }36\sqrt{15}\end{aligned} $$ | |
| ① | $$ \sqrt{45} =
\sqrt{ 3 ^2 \cdot 5 } =
\sqrt{ 3 ^2 } \, \sqrt{ 5 } =
3 \sqrt{ 5 }$$ |
| ② | $$ \sqrt{27} =
\sqrt{ 3 ^2 \cdot 3 } =
\sqrt{ 3 ^2 } \, \sqrt{ 3 } =
3 \sqrt{ 3 }$$ |
| ③ | $$ \color{blue}{ 24 \sqrt{3} } \cdot 3 \sqrt{5} = 72 \sqrt{15} $$$$ \color{blue}{ 2 } \cdot 1 = 2 $$ |
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