Answer
$$\sqrt{180}-4\sqrt{45}=-6\sqrt{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{180}-4\sqrt{45}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}6\sqrt{5}-12\sqrt{5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-6\sqrt{5}\end{aligned} $$ | |
| ① | $$ \sqrt{180} =
\sqrt{ 6 ^2 \cdot 5 } =
\sqrt{ 6 ^2 } \, \sqrt{ 5 } =
6 \sqrt{ 5 }$$ |
| ② | $$ - 4 \sqrt{45} =
-4 \sqrt{ 3 ^2 \cdot 5 } =
-4 \sqrt{ 3 ^2 } \, \sqrt{ 5 } =
-4 \cdot 3 \sqrt{ 5 } =
-12 \sqrt{ 5 } $$ |
| ③ | Combine like terms |
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