Question
Answer
$$-\sqrt{12}+3\sqrt{27}-3\sqrt{20}=7\sqrt{3}-6\sqrt{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-\sqrt{12}+3\sqrt{27}-3\sqrt{20}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-2\sqrt{3}+9\sqrt{3}-6\sqrt{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}7\sqrt{3}-6\sqrt{5}\end{aligned} $$ | |
| ① | $$ - \sqrt{12} =
- \sqrt{ 2 ^2 \cdot 3 } =
- \sqrt{ 2 ^2 } \, \sqrt{ 3 } =
- 2 \sqrt{ 3 }$$ |
| ② | $$ 3 \sqrt{27} =
3 \sqrt{ 3 ^2 \cdot 3 } =
3 \sqrt{ 3 ^2 } \, \sqrt{ 3 } =
3 \cdot 3 \sqrt{ 3 } =
9 \sqrt{ 3 } $$ |
| ③ | $$ - 3 \sqrt{20} =
-3 \sqrt{ 2 ^2 \cdot 5 } =
-3 \sqrt{ 2 ^2 } \, \sqrt{ 5 } =
-3 \cdot 2 \sqrt{ 5 } =
-6 \sqrt{ 5 } $$ |
| ④ | Combine like terms |
This page was created using
Simplify Radical Expression