Question
Answer
$$\dfrac{(289-204\sqrt{2})\cdot(17+12\sqrt{2})}{1}=17$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{(289-204\sqrt{2})\cdot(17+12\sqrt{2})}{1}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{4913+3468\sqrt{2}-3468\sqrt{2}-4896}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}17\end{aligned} $$ | |
| ① | $$ \color{blue}{ \left( 289- 204 \sqrt{2}\right) } \cdot \left( 17 + 12 \sqrt{2}\right) = \color{blue}{289} \cdot17+\color{blue}{289} \cdot 12 \sqrt{2}\color{blue}{- 204 \sqrt{2}} \cdot17\color{blue}{- 204 \sqrt{2}} \cdot 12 \sqrt{2} = \\ = 4913 + 3468 \sqrt{2}- 3468 \sqrt{2}-4896 $$ |
| ② | Remove 1 from denominator. |
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