Answer
$$\sqrt{125}-2\sqrt{45}=-\sqrt{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{125}-2\sqrt{45}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}5\sqrt{5}-6\sqrt{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-\sqrt{5}\end{aligned} $$ | |
| ① | $$ \sqrt{125} =
\sqrt{ 5 ^2 \cdot 5 } =
\sqrt{ 5 ^2 } \, \sqrt{ 5 } =
5 \sqrt{ 5 }$$ |
| ② | $$ - 2 \sqrt{45} =
-2 \sqrt{ 3 ^2 \cdot 5 } =
-2 \sqrt{ 3 ^2 } \, \sqrt{ 5 } =
-2 \cdot 3 \sqrt{ 5 } =
-6 \sqrt{ 5 } $$ |
| ③ | Combine like terms |
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