Answer
$$-3\sqrt{45}+2\sqrt{12}+3\sqrt{6}-3\sqrt{20}=-15\sqrt{5}+4\sqrt{3}+3\sqrt{6}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-3\sqrt{45}+2\sqrt{12}+3\sqrt{6}-3\sqrt{20}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-9\sqrt{5}+4\sqrt{3}+3\sqrt{6}-6\sqrt{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-15\sqrt{5}+4\sqrt{3}+3\sqrt{6}\end{aligned} $$ | |
| ① | $$ - 3 \sqrt{45} =
-3 \sqrt{ 3 ^2 \cdot 5 } =
-3 \sqrt{ 3 ^2 } \, \sqrt{ 5 } =
-3 \cdot 3 \sqrt{ 5 } =
-9 \sqrt{ 5 } $$ |
| ② | $$ 2 \sqrt{12} =
2 \sqrt{ 2 ^2 \cdot 3 } =
2 \sqrt{ 2 ^2 } \, \sqrt{ 3 } =
2 \cdot 2 \sqrt{ 3 } =
4 \sqrt{ 3 } $$ |
| ③ | $$ - 3 \sqrt{20} =
-3 \sqrt{ 2 ^2 \cdot 5 } =
-3 \sqrt{ 2 ^2 } \, \sqrt{ 5 } =
-3 \cdot 2 \sqrt{ 5 } =
-6 \sqrt{ 5 } $$ |
| ④ | Combine like terms |
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