Answer
$$-10\sqrt{45}+5\sqrt{20}=-20\sqrt{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-10\sqrt{45}+5\sqrt{20}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-30\sqrt{5}+10\sqrt{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-20\sqrt{5}\end{aligned} $$ | |
| ① | $$ - 10 \sqrt{45} =
-10 \sqrt{ 3 ^2 \cdot 5 } =
-10 \sqrt{ 3 ^2 } \, \sqrt{ 5 } =
-10 \cdot 3 \sqrt{ 5 } =
-30 \sqrt{ 5 } $$ |
| ② | $$ 5 \sqrt{20} =
5 \sqrt{ 2 ^2 \cdot 5 } =
5 \sqrt{ 2 ^2 } \, \sqrt{ 5 } =
5 \cdot 2 \sqrt{ 5 } =
10 \sqrt{ 5 } $$ |
| ③ | Combine like terms |
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