Question
Answer
$$2\sqrt{27}-8\sqrt{108}=-42\sqrt{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2\sqrt{27}-8\sqrt{108}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}6\sqrt{3}-48\sqrt{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-42\sqrt{3}\end{aligned} $$ | |
| ① | $$ 2 \sqrt{27} =
2 \sqrt{ 3 ^2 \cdot 3 } =
2 \sqrt{ 3 ^2 } \, \sqrt{ 3 } =
2 \cdot 3 \sqrt{ 3 } =
6 \sqrt{ 3 } $$ |
| ② | $$ - 8 \sqrt{108} =
-8 \sqrt{ 6 ^2 \cdot 3 } =
-8 \sqrt{ 6 ^2 } \, \sqrt{ 3 } =
-8 \cdot 6 \sqrt{ 3 } =
-48 \sqrt{ 3 } $$ |
| ③ | Combine like terms |
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