Question
Answer
$$3\sqrt{162}^2=486$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3\sqrt{162}^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}3(9\sqrt{2})^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3\cdot162 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}486\end{aligned} $$ | |
| ① | $$ \sqrt{162} =
\sqrt{ 9 ^2 \cdot 2 } =
\sqrt{ 9 ^2 } \, \sqrt{ 2 } =
9 \sqrt{ 2 }$$ |
| ② | $$ (9\sqrt{2})^2 =
9^{ 2 } \cdot \sqrt{2} ^ { 2 } =
9^{ 2 } \sqrt{2} ^2 =
9^{ 2 } \lvert 2 \rvert =
162 $$ |
| ③ | $ 3 \cdot 162 = 486 $ |
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