Question
Answer
$$5\sqrt{27}-\sqrt{108}+2\sqrt{75}=19\sqrt{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}5\sqrt{27}-\sqrt{108}+2\sqrt{75}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}15\sqrt{3}-6\sqrt{3}+10\sqrt{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}19\sqrt{3}\end{aligned} $$ | |
| ① | $$ 5 \sqrt{27} =
5 \sqrt{ 3 ^2 \cdot 3 } =
5 \sqrt{ 3 ^2 } \, \sqrt{ 3 } =
5 \cdot 3 \sqrt{ 3 } =
15 \sqrt{ 3 } $$ |
| ② | $$ - \sqrt{108} =
- \sqrt{ 6 ^2 \cdot 3 } =
- \sqrt{ 6 ^2 } \, \sqrt{ 3 } =
- 6 \sqrt{ 3 }$$ |
| ③ | $$ 2 \sqrt{75} =
2 \sqrt{ 5 ^2 \cdot 3 } =
2 \sqrt{ 5 ^2 } \, \sqrt{ 3 } =
2 \cdot 5 \sqrt{ 3 } =
10 \sqrt{ 3 } $$ |
| ④ | Combine like terms |
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