Question
Answer
$$\dfrac{-6}{\sqrt{6}+\sqrt{35}}=\dfrac{6\sqrt{6}-6\sqrt{35}}{29}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{-6}{\sqrt{6}+\sqrt{35}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{-6}{\sqrt{6}+\sqrt{35}}\frac{\sqrt{6}-\sqrt{35}}{\sqrt{6}-\sqrt{35}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-6\sqrt{6}+6\sqrt{35}}{6-\sqrt{210}+\sqrt{210}-35} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-6\sqrt{6}+6\sqrt{35}}{-29} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{6\sqrt{6}-6\sqrt{35}}{29}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{6}- \sqrt{35}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ -6 } \cdot \left( \sqrt{6}- \sqrt{35}\right) = \color{blue}{-6} \cdot \sqrt{6}\color{blue}{-6} \cdot- \sqrt{35} = \\ = - 6 \sqrt{6} + 6 \sqrt{35} $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{6} + \sqrt{35}\right) } \cdot \left( \sqrt{6}- \sqrt{35}\right) = \color{blue}{ \sqrt{6}} \cdot \sqrt{6}+\color{blue}{ \sqrt{6}} \cdot- \sqrt{35}+\color{blue}{ \sqrt{35}} \cdot \sqrt{6}+\color{blue}{ \sqrt{35}} \cdot- \sqrt{35} = \\ = 6- \sqrt{210} + \sqrt{210}-35 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Multiply both numerator and denominator by -1. |
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