Question
Answer
$$\dfrac{72}{3\sqrt{11}+5}=\dfrac{216\sqrt{11}-360}{74}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{72}{3\sqrt{11}+5}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{72}{3\sqrt{11}+5}\frac{3\sqrt{11}-5}{3\sqrt{11}-5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{216\sqrt{11}-360}{99-15\sqrt{11}+15\sqrt{11}-25} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{216\sqrt{11}-360}{74}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 3 \sqrt{11}-5} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 72 } \cdot \left( 3 \sqrt{11}-5\right) = \color{blue}{72} \cdot 3 \sqrt{11}+\color{blue}{72} \cdot-5 = \\ = 216 \sqrt{11}-360 $$ Simplify denominator. $$ \color{blue}{ \left( 3 \sqrt{11} + 5\right) } \cdot \left( 3 \sqrt{11}-5\right) = \color{blue}{ 3 \sqrt{11}} \cdot 3 \sqrt{11}+\color{blue}{ 3 \sqrt{11}} \cdot-5+\color{blue}{5} \cdot 3 \sqrt{11}+\color{blue}{5} \cdot-5 = \\ = 99- 15 \sqrt{11} + 15 \sqrt{11}-25 $$ |
| ③ | Simplify numerator and denominator |
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