Question
Answer
$$5\cdot\dfrac{\sqrt{108}}{2}\sqrt{125}=75\sqrt{15}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}5 \cdot \frac{\sqrt{108}}{2}\sqrt{125}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}5 \cdot \frac{\sqrt{108}}{2}\cdot5\sqrt{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}5 \cdot \frac{6\sqrt{3}}{2}\cdot5\sqrt{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{150\sqrt{15}}{2} \xlongequal{ } \\[1 em] & \xlongequal{ }75\sqrt{15}\end{aligned} $$ | |
| ① | $$ \sqrt{125} =
\sqrt{ 5 ^2 \cdot 5 } =
\sqrt{ 5 ^2 } \, \sqrt{ 5 } =
5 \sqrt{ 5 }$$ |
| ② | $$ \sqrt{108} =
\sqrt{ 6 ^2 \cdot 3 } =
\sqrt{ 6 ^2 } \, \sqrt{ 3 } =
6 \sqrt{ 3 }$$ |
| ③ | $$ \color{blue}{ 30 \sqrt{3} } \cdot 5 \sqrt{5} = 150 \sqrt{15} $$$$ \color{blue}{ 2 } \cdot 1 = 2 $$ |
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