Answer
$$-\sqrt{45}-3\sqrt{20}+2\sqrt{125}=\sqrt{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-\sqrt{45}-3\sqrt{20}+2\sqrt{125}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-3\sqrt{5}-6\sqrt{5}+10\sqrt{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\sqrt{5}\end{aligned} $$ | |
| ① | $$ - \sqrt{45} =
- \sqrt{ 3 ^2 \cdot 5 } =
- \sqrt{ 3 ^2 } \, \sqrt{ 5 } =
- 3 \sqrt{ 5 }$$ |
| ② | $$ - 3 \sqrt{20} =
-3 \sqrt{ 2 ^2 \cdot 5 } =
-3 \sqrt{ 2 ^2 } \, \sqrt{ 5 } =
-3 \cdot 2 \sqrt{ 5 } =
-6 \sqrt{ 5 } $$ |
| ③ | $$ 2 \sqrt{125} =
2 \sqrt{ 5 ^2 \cdot 5 } =
2 \sqrt{ 5 ^2 } \, \sqrt{ 5 } =
2 \cdot 5 \sqrt{ 5 } =
10 \sqrt{ 5 } $$ |
| ④ | Combine like terms |
This page was created using
Simplify Radical Expression