Question
Answer
$$(-5+2\sqrt{6})\cdot(-6-3\sqrt{54})=-78+33\sqrt{6}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-5+2\sqrt{6})\cdot(-6-3\sqrt{54})& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(-5+2\sqrt{6})\cdot(-6-9\sqrt{6}) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}30+45\sqrt{6}-12\sqrt{6}-108 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-78+33\sqrt{6}\end{aligned} $$ | |
| ① | $$ - 3 \sqrt{54} =
-3 \sqrt{ 3 ^2 \cdot 6 } =
-3 \sqrt{ 3 ^2 } \, \sqrt{ 6 } =
-3 \cdot 3 \sqrt{ 6 } =
-9 \sqrt{ 6 } $$ |
| ② | $$ \color{blue}{ \left( -5 + 2 \sqrt{6}\right) } \cdot \left( -6- 9 \sqrt{6}\right) = \color{blue}{-5} \cdot-6\color{blue}{-5} \cdot- 9 \sqrt{6}+\color{blue}{ 2 \sqrt{6}} \cdot-6+\color{blue}{ 2 \sqrt{6}} \cdot- 9 \sqrt{6} = \\ = 30 + 45 \sqrt{6}- 12 \sqrt{6}-108 $$ |
| ③ | Combine like terms |
This page was created using
Simplify Radical Expression