Question
Answer
$$-3\sqrt{18}+3\sqrt{20}-\sqrt{8}=-11\sqrt{2}+6\sqrt{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-3\sqrt{18}+3\sqrt{20}-\sqrt{8}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-9\sqrt{2}+6\sqrt{5}-2\sqrt{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-11\sqrt{2}+6\sqrt{5}\end{aligned} $$ | |
| ① | $$ - 3 \sqrt{18} =
-3 \sqrt{ 3 ^2 \cdot 2 } =
-3 \sqrt{ 3 ^2 } \, \sqrt{ 2 } =
-3 \cdot 3 \sqrt{ 2 } =
-9 \sqrt{ 2 } $$ |
| ② | $$ 3 \sqrt{20} =
3 \sqrt{ 2 ^2 \cdot 5 } =
3 \sqrt{ 2 ^2 } \, \sqrt{ 5 } =
3 \cdot 2 \sqrt{ 5 } =
6 \sqrt{ 5 } $$ |
| ③ | $$ - \sqrt{8} =
- \sqrt{ 2 ^2 \cdot 2 } =
- \sqrt{ 2 ^2 } \, \sqrt{ 2 } =
- 2 \sqrt{ 2 }$$ |
| ④ | Combine like terms |
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