Question
Answer
$$5\sqrt{12}^3-3^2\sqrt{147}=57\sqrt{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}5\sqrt{12}^3-3^2\sqrt{147}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}5(2\sqrt{3})^3-3^2\cdot7\sqrt{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}5\cdot24\sqrt{3}-9\cdot7\sqrt{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}57\sqrt{3}\end{aligned} $$ | |
| ① | $$ \sqrt{12} =
\sqrt{ 2 ^2 \cdot 3 } =
\sqrt{ 2 ^2 } \, \sqrt{ 3 } =
2 \sqrt{ 3 }$$ |
| ② | $$ \sqrt{147} =
\sqrt{ 7 ^2 \cdot 3 } =
\sqrt{ 7 ^2 } \, \sqrt{ 3 } =
7 \sqrt{ 3 }$$ |
| ③ | $$ (2\sqrt{3})^3 =
2^{ 3 } \cdot \sqrt{3} ^ { 3 } =
2^{ 3 } \sqrt{3} ^2 \cdot \sqrt{3} =
2^{ 3 } \lvert 3 \rvert \cdot \sqrt{3} =
24\sqrt{3} $$$ 3 ^ 2 = 9 $ |
| ④ | Combine like terms |
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