Answer
$$3\sqrt{10}+\sqrt{75}-2\sqrt{40}-4\sqrt{12}=-\sqrt{10}-3\sqrt{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3\sqrt{10}+\sqrt{75}-2\sqrt{40}-4\sqrt{12}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}3\sqrt{10}+5\sqrt{3}-4\sqrt{10}-8\sqrt{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-\sqrt{10}-3\sqrt{3}\end{aligned} $$ | |
| ① | $$ \sqrt{75} =
\sqrt{ 5 ^2 \cdot 3 } =
\sqrt{ 5 ^2 } \, \sqrt{ 3 } =
5 \sqrt{ 3 }$$ |
| ② | $$ - 2 \sqrt{40} =
-2 \sqrt{ 2 ^2 \cdot 10 } =
-2 \sqrt{ 2 ^2 } \, \sqrt{ 10 } =
-2 \cdot 2 \sqrt{ 10 } =
-4 \sqrt{ 10 } $$ |
| ③ | $$ - 4 \sqrt{12} =
-4 \sqrt{ 2 ^2 \cdot 3 } =
-4 \sqrt{ 2 ^2 } \, \sqrt{ 3 } =
-4 \cdot 2 \sqrt{ 3 } =
-8 \sqrt{ 3 } $$ |
| ④ | Combine like terms |
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