Question
Answer
$$\sqrt{600}-4\sqrt{96}+2\sqrt{24}=-2\sqrt{6}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{600}-4\sqrt{96}+2\sqrt{24}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}10\sqrt{6}-16\sqrt{6}+4\sqrt{6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-2\sqrt{6}\end{aligned} $$ | |
| ① | $$ \sqrt{600} =
\sqrt{ 10 ^2 \cdot 6 } =
\sqrt{ 10 ^2 } \, \sqrt{ 6 } =
10 \sqrt{ 6 }$$ |
| ② | $$ - 4 \sqrt{96} =
-4 \sqrt{ 4 ^2 \cdot 6 } =
-4 \sqrt{ 4 ^2 } \, \sqrt{ 6 } =
-4 \cdot 4 \sqrt{ 6 } =
-16 \sqrt{ 6 } $$ |
| ③ | $$ 2 \sqrt{24} =
2 \sqrt{ 2 ^2 \cdot 6 } =
2 \sqrt{ 2 ^2 } \, \sqrt{ 6 } =
2 \cdot 2 \sqrt{ 6 } =
4 \sqrt{ 6 } $$ |
| ④ | Combine like terms |
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