Question
Answer
$$\dfrac{\sqrt{8}}{\sqrt{2}-\sqrt{8}}=-2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{8}}{\sqrt{2}-\sqrt{8}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{8}}{\sqrt{2}-\sqrt{8}}\frac{\sqrt{2}+\sqrt{8}}{\sqrt{2}+\sqrt{8}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{4+8}{2+4-4-8} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{12}{-6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-\frac{12}{6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}- \, \frac{ 12 : \color{orangered}{ 6 } }{ 6 : \color{orangered}{ 6 }} \xlongequal{ } \\[1 em] & \xlongequal{ }-\frac{2}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}-2\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{2} + \sqrt{8}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \sqrt{8} } \cdot \left( \sqrt{2} + \sqrt{8}\right) = \color{blue}{ \sqrt{8}} \cdot \sqrt{2}+\color{blue}{ \sqrt{8}} \cdot \sqrt{8} = \\ = 4 + 8 $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{2}- \sqrt{8}\right) } \cdot \left( \sqrt{2} + \sqrt{8}\right) = \color{blue}{ \sqrt{2}} \cdot \sqrt{2}+\color{blue}{ \sqrt{2}} \cdot \sqrt{8}\color{blue}{- \sqrt{8}} \cdot \sqrt{2}\color{blue}{- \sqrt{8}} \cdot \sqrt{8} = \\ = 2 + 4-4-8 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Place minus sign in front of the fraction. |
| ⑤ | Divide both the top and bottom numbers by $ \color{orangered}{ 6 } $. |
| ⑥ | Remove 1 from denominator. |
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