Answer
$$\sqrt{180}-5\sqrt{12}\sqrt{20}=6\sqrt{5}-20\sqrt{15}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{180}-5\sqrt{12}\sqrt{20}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}6\sqrt{5}-20\sqrt{15}\end{aligned} $$ | |
| ① | $$ \sqrt{180} =
\sqrt{ 6 ^2 \cdot 5 } =
\sqrt{ 6 ^2 } \, \sqrt{ 5 } =
6 \sqrt{ 5 }$$ |
| ② | $$ - 5 \sqrt{240} =
-5 \sqrt{ 4 ^2 \cdot 15 } =
-5 \sqrt{ 4 ^2 } \, \sqrt{ 15 } =
-5 \cdot 4 \sqrt{ 15 } =
-20 \sqrt{ 15 } $$ |
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