Question
Answer
$$\dfrac{2}{3\sqrt{5}+2\sqrt{11}}=6\sqrt{5}-4\sqrt{11}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2}{3\sqrt{5}+2\sqrt{11}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2}{3\sqrt{5}+2\sqrt{11}}\frac{3\sqrt{5}-2\sqrt{11}}{3\sqrt{5}-2\sqrt{11}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{6\sqrt{5}-4\sqrt{11}}{45-6\sqrt{55}+6\sqrt{55}-44} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{6\sqrt{5}-4\sqrt{11}}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}6\sqrt{5}-4\sqrt{11}\end{aligned} $$ | |
| 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. $$ \color{blue}{ 2 } \cdot \left( 3 \sqrt{5}- 2 \sqrt{11}\right) = \color{blue}{2} \cdot 3 \sqrt{5}+\color{blue}{2} \cdot- 2 \sqrt{11} = \\ = 6 \sqrt{5}- 4 \sqrt{11} $$ 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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