Question
Answer
$$(2\sqrt{3}-\sqrt{10})(\sqrt{6}-7\sqrt{20})=76\sqrt{2}-30\sqrt{15}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2\sqrt{3}-\sqrt{10})(\sqrt{6}-7\sqrt{20})& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(2\sqrt{3}-\sqrt{10})(\sqrt{6}-14\sqrt{5}) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}6\sqrt{2}-28\sqrt{15}-2\sqrt{15}+70\sqrt{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}76\sqrt{2}-30\sqrt{15}\end{aligned} $$ | |
| ① | $$ - 7 \sqrt{20} =
-7 \sqrt{ 2 ^2 \cdot 5 } =
-7 \sqrt{ 2 ^2 } \, \sqrt{ 5 } =
-7 \cdot 2 \sqrt{ 5 } =
-14 \sqrt{ 5 } $$ |
| ② | $$ \color{blue}{ \left( 2 \sqrt{3}- \sqrt{10}\right) } \cdot \left( \sqrt{6}- 14 \sqrt{5}\right) = \color{blue}{ 2 \sqrt{3}} \cdot \sqrt{6}+\color{blue}{ 2 \sqrt{3}} \cdot- 14 \sqrt{5}\color{blue}{- \sqrt{10}} \cdot \sqrt{6}\color{blue}{- \sqrt{10}} \cdot- 14 \sqrt{5} = \\ = 6 \sqrt{2}- 28 \sqrt{15}- 2 \sqrt{15} + 70 \sqrt{2} $$ |
| ③ | Combine like terms |
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