Question
Answer
$$7\sqrt{72}+\sqrt{54}-2\sqrt{162}=24\sqrt{2}+3\sqrt{6}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}7\sqrt{72}+\sqrt{54}-2\sqrt{162}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}42\sqrt{2}+3\sqrt{6}-18\sqrt{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}24\sqrt{2}+3\sqrt{6}\end{aligned} $$ | |
| ① | $$ 7 \sqrt{72} =
7 \sqrt{ 6 ^2 \cdot 2 } =
7 \sqrt{ 6 ^2 } \, \sqrt{ 2 } =
7 \cdot 6 \sqrt{ 2 } =
42 \sqrt{ 2 } $$ |
| ② | $$ \sqrt{54} =
\sqrt{ 3 ^2 \cdot 6 } =
\sqrt{ 3 ^2 } \, \sqrt{ 6 } =
3 \sqrt{ 6 }$$ |
| ③ | $$ - 2 \sqrt{162} =
-2 \sqrt{ 9 ^2 \cdot 2 } =
-2 \sqrt{ 9 ^2 } \, \sqrt{ 2 } =
-2 \cdot 9 \sqrt{ 2 } =
-18 \sqrt{ 2 } $$ |
| ④ | Combine like terms |
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