Question
Answer
$$4\sqrt{75}+3\sqrt{48}-\sqrt{32}=32\sqrt{3}-4\sqrt{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}4\sqrt{75}+3\sqrt{48}-\sqrt{32}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}20\sqrt{3}+12\sqrt{3}-4\sqrt{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}32\sqrt{3}-4\sqrt{2}\end{aligned} $$ | |
| ① | $$ 4 \sqrt{75} =
4 \sqrt{ 5 ^2 \cdot 3 } =
4 \sqrt{ 5 ^2 } \, \sqrt{ 3 } =
4 \cdot 5 \sqrt{ 3 } =
20 \sqrt{ 3 } $$ |
| ② | $$ 3 \sqrt{48} =
3 \sqrt{ 4 ^2 \cdot 3 } =
3 \sqrt{ 4 ^2 } \, \sqrt{ 3 } =
3 \cdot 4 \sqrt{ 3 } =
12 \sqrt{ 3 } $$ |
| ③ | $$ - \sqrt{32} =
- \sqrt{ 4 ^2 \cdot 2 } =
- \sqrt{ 4 ^2 } \, \sqrt{ 2 } =
- 4 \sqrt{ 2 }$$ |
| ④ | Combine like terms |
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