Question
Answer
$$\dfrac{12\sqrt{11}}{3\sqrt{5}-2\sqrt{11}}=36\sqrt{55}+264$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{12\sqrt{11}}{3\sqrt{5}-2\sqrt{11}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{12\sqrt{11}}{3\sqrt{5}-2\sqrt{11}}\frac{3\sqrt{5}+2\sqrt{11}}{3\sqrt{5}+2\sqrt{11}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{36\sqrt{55}+264}{45+6\sqrt{55}-6\sqrt{55}-44} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{36\sqrt{55}+264}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}36\sqrt{55}+264\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 3 \sqrt{5} + 2 \sqrt{11}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 12 \sqrt{11} } \cdot \left( 3 \sqrt{5} + 2 \sqrt{11}\right) = \color{blue}{ 12 \sqrt{11}} \cdot 3 \sqrt{5}+\color{blue}{ 12 \sqrt{11}} \cdot 2 \sqrt{11} = \\ = 36 \sqrt{55} + 264 $$ Simplify denominator. $$ \color{blue}{ \left( 3 \sqrt{5}- 2 \sqrt{11}\right) } \cdot \left( 3 \sqrt{5} + 2 \sqrt{11}\right) = \color{blue}{ 3 \sqrt{5}} \cdot 3 \sqrt{5}+\color{blue}{ 3 \sqrt{5}} \cdot 2 \sqrt{11}\color{blue}{- 2 \sqrt{11}} \cdot 3 \sqrt{5}\color{blue}{- 2 \sqrt{11}} \cdot 2 \sqrt{11} = \\ = 45 + 6 \sqrt{55}- 6 \sqrt{55}-44 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Remove 1 from denominator. |
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