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