Question
Answer
$$\dfrac{9}{6-\sqrt{8}}=\dfrac{54+18\sqrt{2}}{28}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{9}{6-\sqrt{8}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{9}{6-\sqrt{8}}\frac{6+\sqrt{8}}{6+\sqrt{8}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{54+18\sqrt{2}}{36+12\sqrt{2}-12\sqrt{2}-8} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{54+18\sqrt{2}}{28}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 6 + \sqrt{8}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 9 } \cdot \left( 6 + \sqrt{8}\right) = \color{blue}{9} \cdot6+\color{blue}{9} \cdot \sqrt{8} = \\ = 54 + 18 \sqrt{2} $$ Simplify denominator. $$ \color{blue}{ \left( 6- \sqrt{8}\right) } \cdot \left( 6 + \sqrt{8}\right) = \color{blue}{6} \cdot6+\color{blue}{6} \cdot \sqrt{8}\color{blue}{- \sqrt{8}} \cdot6\color{blue}{- \sqrt{8}} \cdot \sqrt{8} = \\ = 36 + 12 \sqrt{2}- 12 \sqrt{2}-8 $$ |
| ③ | Simplify numerator and denominator |
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