Question
Answer
$$\dfrac{(-10+\sqrt{2})\cdot(6+\sqrt{2})}{1}=-58-4\sqrt{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{(-10+\sqrt{2})\cdot(6+\sqrt{2})}{1}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{-60-10\sqrt{2}+6\sqrt{2}+2}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-58-4\sqrt{2}\end{aligned} $$ | |
| ① | $$ \color{blue}{ \left( -10 + \sqrt{2}\right) } \cdot \left( 6 + \sqrt{2}\right) = \color{blue}{-10} \cdot6\color{blue}{-10} \cdot \sqrt{2}+\color{blue}{ \sqrt{2}} \cdot6+\color{blue}{ \sqrt{2}} \cdot \sqrt{2} = \\ = -60- 10 \sqrt{2} + 6 \sqrt{2} + 2 $$ |
| ② | Remove 1 from denominator. |
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