Question
Answer
$$\dfrac{2}{3}\sqrt{27}+\dfrac{1}{2}\sqrt{48}-4\sqrt{3}=0$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2}{3}\sqrt{27}+\frac{1}{2}\sqrt{48}-4\sqrt{3}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2\sqrt{3}+2\sqrt{3}-4\sqrt{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}0\end{aligned} $$ | |
| ① | $$ \frac{ 2 }{ 3 } \sqrt{ 27 } =
\frac{ 2 }{ 3 } \sqrt{ 3 ^2 \cdot 3 } =
\frac{ 2 }{ 3 } \sqrt{ 3 ^2 } \, \sqrt{ 3 } =
\frac{ 2 }{ 3 } \cdot 3 \sqrt{ 3 } =
2 \sqrt{ 3 } $$ |
| ② | $$ \frac{ 1 }{ 2 } \sqrt{ 48 } =
\frac{ 1 }{ 2 } \sqrt{ 4 ^2 \cdot 3 } =
\frac{ 1 }{ 2 } \sqrt{ 4 ^2 } \, \sqrt{ 3 } =
\frac{ 1 }{ 2 } \cdot 4 \sqrt{ 3 } =
2 \sqrt{ 3 } $$ |
| ③ | Combine like terms |
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