Question
Answer
$$6\sqrt{40}-2\sqrt{90}-3\sqrt{160}=-6\sqrt{10}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}6\sqrt{40}-2\sqrt{90}-3\sqrt{160}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}12\sqrt{10}-6\sqrt{10}-12\sqrt{10} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-6\sqrt{10}\end{aligned} $$ | |
| ① | $$ 6 \sqrt{40} =
6 \sqrt{ 2 ^2 \cdot 10 } =
6 \sqrt{ 2 ^2 } \, \sqrt{ 10 } =
6 \cdot 2 \sqrt{ 10 } =
12 \sqrt{ 10 } $$ |
| ② | $$ - 2 \sqrt{90} =
-2 \sqrt{ 3 ^2 \cdot 10 } =
-2 \sqrt{ 3 ^2 } \, \sqrt{ 10 } =
-2 \cdot 3 \sqrt{ 10 } =
-6 \sqrt{ 10 } $$ |
| ③ | $$ - 3 \sqrt{160} =
-3 \sqrt{ 4 ^2 \cdot 10 } =
-3 \sqrt{ 4 ^2 } \, \sqrt{ 10 } =
-3 \cdot 4 \sqrt{ 10 } =
-12 \sqrt{ 10 } $$ |
| ④ | Combine like terms |
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