Question
Answer
$$\dfrac{6}{9-\sqrt{10}}=\dfrac{54+6\sqrt{10}}{71}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{6}{9-\sqrt{10}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{6}{9-\sqrt{10}}\frac{9+\sqrt{10}}{9+\sqrt{10}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{54+6\sqrt{10}}{81+9\sqrt{10}-9\sqrt{10}-10} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{54+6\sqrt{10}}{71}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 9 + \sqrt{10}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 6 } \cdot \left( 9 + \sqrt{10}\right) = \color{blue}{6} \cdot9+\color{blue}{6} \cdot \sqrt{10} = \\ = 54 + 6 \sqrt{10} $$ Simplify denominator. $$ \color{blue}{ \left( 9- \sqrt{10}\right) } \cdot \left( 9 + \sqrt{10}\right) = \color{blue}{9} \cdot9+\color{blue}{9} \cdot \sqrt{10}\color{blue}{- \sqrt{10}} \cdot9\color{blue}{- \sqrt{10}} \cdot \sqrt{10} = \\ = 81 + 9 \sqrt{10}- 9 \sqrt{10}-10 $$ |
| ③ | Simplify numerator and denominator |
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