Question
Answer
$$\dfrac{2}{-10\sqrt{2}+\sqrt{35}}=\dfrac{-20\sqrt{2}-2\sqrt{35}}{165}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2}{-10\sqrt{2}+\sqrt{35}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2}{-10\sqrt{2}+\sqrt{35}}\frac{-10\sqrt{2}-\sqrt{35}}{-10\sqrt{2}-\sqrt{35}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-20\sqrt{2}-2\sqrt{35}}{200+10\sqrt{70}-10\sqrt{70}-35} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-20\sqrt{2}-2\sqrt{35}}{165}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ - 10 \sqrt{2}- \sqrt{35}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 2 } \cdot \left( - 10 \sqrt{2}- \sqrt{35}\right) = \color{blue}{2} \cdot- 10 \sqrt{2}+\color{blue}{2} \cdot- \sqrt{35} = \\ = - 20 \sqrt{2}- 2 \sqrt{35} $$ Simplify denominator. $$ \color{blue}{ \left( - 10 \sqrt{2} + \sqrt{35}\right) } \cdot \left( - 10 \sqrt{2}- \sqrt{35}\right) = \color{blue}{- 10 \sqrt{2}} \cdot- 10 \sqrt{2}\color{blue}{- 10 \sqrt{2}} \cdot- \sqrt{35}+\color{blue}{ \sqrt{35}} \cdot- 10 \sqrt{2}+\color{blue}{ \sqrt{35}} \cdot- \sqrt{35} = \\ = 200 + 10 \sqrt{70}- 10 \sqrt{70}-35 $$ |
| ③ | Simplify numerator and denominator |
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