Question
Answer
$$3(\sqrt{5}-2)-2(\sqrt{20}+3)=-\sqrt{5}-12$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3(\sqrt{5}-2)-2(\sqrt{20}+3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}3(\sqrt{5}-2)-2(2\sqrt{5}+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3\sqrt{5}-6-(4\sqrt{5}+6) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}3\sqrt{5}-6-4\sqrt{5}-6 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-\sqrt{5}-12\end{aligned} $$ | |
| ① | $$ \sqrt{20} =
\sqrt{ 2 ^2 \cdot 5 } =
\sqrt{ 2 ^2 } \, \sqrt{ 5 } =
2 \sqrt{ 5 }$$ |
| ② | $$ \color{blue}{ 3 } \cdot \left( \sqrt{5}-2\right) = \color{blue}{3} \cdot \sqrt{5}+\color{blue}{3} \cdot-2 = \\ = 3 \sqrt{5}-6 $$$$ \color{blue}{ 2 } \cdot \left( 2 \sqrt{5} + 3\right) = \color{blue}{2} \cdot 2 \sqrt{5}+\color{blue}{2} \cdot3 = \\ = 4 \sqrt{5} + 6 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ -\left( 4 \sqrt{5} + 6 \right) = - 4 \sqrt{5}-6 $$ |
| ④ | Combine like terms |
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