Answer
$$\sqrt{60}\cdot(2\sqrt{10}+3\sqrt{2})=20\sqrt{6}+6\sqrt{30}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{60}\cdot(2\sqrt{10}+3\sqrt{2})& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2\sqrt{15}(2\sqrt{10}+3\sqrt{2}) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}20\sqrt{6}+6\sqrt{30}\end{aligned} $$ | |
| ① | $$ \sqrt{60} =
\sqrt{ 2 ^2 \cdot 15 } =
\sqrt{ 2 ^2 } \, \sqrt{ 15 } =
2 \sqrt{ 15 }$$ |
| ② | $$ \color{blue}{ 2 \sqrt{15} } \cdot \left( 2 \sqrt{10} + 3 \sqrt{2}\right) = \color{blue}{ 2 \sqrt{15}} \cdot 2 \sqrt{10}+\color{blue}{ 2 \sqrt{15}} \cdot 3 \sqrt{2} = \\ = 20 \sqrt{6} + 6 \sqrt{30} $$ |
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