Question
Answer
$$\dfrac{(\sqrt{15}+2\sqrt{3})(\sqrt{15}-2\sqrt{3})}{1}=3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{(\sqrt{15}+2\sqrt{3})(\sqrt{15}-2\sqrt{3})}{1}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{15-6\sqrt{5}+6\sqrt{5}-12}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3\end{aligned} $$ | |
| ① | $$ \color{blue}{ \left( \sqrt{15} + 2 \sqrt{3}\right) } \cdot \left( \sqrt{15}- 2 \sqrt{3}\right) = \color{blue}{ \sqrt{15}} \cdot \sqrt{15}+\color{blue}{ \sqrt{15}} \cdot- 2 \sqrt{3}+\color{blue}{ 2 \sqrt{3}} \cdot \sqrt{15}+\color{blue}{ 2 \sqrt{3}} \cdot- 2 \sqrt{3} = \\ = 15- 6 \sqrt{5} + 6 \sqrt{5}-12 $$ |
| ② | Remove 1 from denominator. |
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