Question
Answer
$$\dfrac{(3+\sqrt{5})\cdot(3+\sqrt{5})}{1}=14+6\sqrt{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{(3+\sqrt{5})\cdot(3+\sqrt{5})}{1}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{9+3\sqrt{5}+3\sqrt{5}+5}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}14+6\sqrt{5}\end{aligned} $$ | |
| ① | $$ \color{blue}{ \left( 3 + \sqrt{5}\right) } \cdot \left( 3 + \sqrt{5}\right) = \color{blue}{3} \cdot3+\color{blue}{3} \cdot \sqrt{5}+\color{blue}{ \sqrt{5}} \cdot3+\color{blue}{ \sqrt{5}} \cdot \sqrt{5} = \\ = 9 + 3 \sqrt{5} + 3 \sqrt{5} + 5 $$ |
| ② | Remove 1 from denominator. |
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