Question
Answer
$$\dfrac{\sqrt{6}}{\sqrt{2}+53}=\dfrac{-2\sqrt{3}+53\sqrt{6}}{2807}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{6}}{\sqrt{2}+53}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{6}}{\sqrt{2}+53}\frac{\sqrt{2}-53}{\sqrt{2}-53} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{2\sqrt{3}-53\sqrt{6}}{2-53\sqrt{2}+53\sqrt{2}-2809} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{2\sqrt{3}-53\sqrt{6}}{-2807} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-2\sqrt{3}+53\sqrt{6}}{2807}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{2}-53} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \sqrt{6} } \cdot \left( \sqrt{2}-53\right) = \color{blue}{ \sqrt{6}} \cdot \sqrt{2}+\color{blue}{ \sqrt{6}} \cdot-53 = \\ = 2 \sqrt{3}- 53 \sqrt{6} $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{2} + 53\right) } \cdot \left( \sqrt{2}-53\right) = \color{blue}{ \sqrt{2}} \cdot \sqrt{2}+\color{blue}{ \sqrt{2}} \cdot-53+\color{blue}{53} \cdot \sqrt{2}+\color{blue}{53} \cdot-53 = \\ = 2- 53 \sqrt{2} + 53 \sqrt{2}-2809 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Multiply both numerator and denominator by -1. |
This page was created using
Rationalize Denominator Calculator