Question
Answer
$$-2\sqrt{32}-4\sqrt{6}+2\sqrt{128}+4\sqrt{48}=8\sqrt{2}-4\sqrt{6}+16\sqrt{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-2\sqrt{32}-4\sqrt{6}+2\sqrt{128}+4\sqrt{48}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-8\sqrt{2}-4\sqrt{6}+16\sqrt{2}+16\sqrt{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}8\sqrt{2}-4\sqrt{6}+16\sqrt{3}\end{aligned} $$ | |
| ① | $$ - 2 \sqrt{32} =
-2 \sqrt{ 4 ^2 \cdot 2 } =
-2 \sqrt{ 4 ^2 } \, \sqrt{ 2 } =
-2 \cdot 4 \sqrt{ 2 } =
-8 \sqrt{ 2 } $$ |
| ② | $$ 2 \sqrt{128} =
2 \sqrt{ 8 ^2 \cdot 2 } =
2 \sqrt{ 8 ^2 } \, \sqrt{ 2 } =
2 \cdot 8 \sqrt{ 2 } =
16 \sqrt{ 2 } $$ |
| ③ | $$ 4 \sqrt{48} =
4 \sqrt{ 4 ^2 \cdot 3 } =
4 \sqrt{ 4 ^2 } \, \sqrt{ 3 } =
4 \cdot 4 \sqrt{ 3 } =
16 \sqrt{ 3 } $$ |
| ④ | Combine like terms |
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