Answer
$$4\sqrt{125}-2\sqrt{243}-3\sqrt{20}+5\sqrt{27}=14\sqrt{5}-3\sqrt{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}4\sqrt{125}-2\sqrt{243}-3\sqrt{20}+5\sqrt{27}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}20\sqrt{5}-18\sqrt{3}-6\sqrt{5}+15\sqrt{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}14\sqrt{5}-3\sqrt{3}\end{aligned} $$ | |
| ① | $$ 4 \sqrt{125} =
4 \sqrt{ 5 ^2 \cdot 5 } =
4 \sqrt{ 5 ^2 } \, \sqrt{ 5 } =
4 \cdot 5 \sqrt{ 5 } =
20 \sqrt{ 5 } $$ |
| ② | $$ - 2 \sqrt{243} =
-2 \sqrt{ 9 ^2 \cdot 3 } =
-2 \sqrt{ 9 ^2 } \, \sqrt{ 3 } =
-2 \cdot 9 \sqrt{ 3 } =
-18 \sqrt{ 3 } $$ |
| 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 | $$ 5 \sqrt{27} =
5 \sqrt{ 3 ^2 \cdot 3 } =
5 \sqrt{ 3 ^2 } \, \sqrt{ 3 } =
5 \cdot 3 \sqrt{ 3 } =
15 \sqrt{ 3 } $$ |
| ⑤ | Combine like terms |
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