Question
Answer
$$\dfrac{1}{49+20\sqrt{6}}=49-20\sqrt{6}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{1}{49+20\sqrt{6}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{1}{49+20\sqrt{6}}\frac{49-20\sqrt{6}}{49-20\sqrt{6}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{49-20\sqrt{6}}{2401-980\sqrt{6}+980\sqrt{6}-2400} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{49-20\sqrt{6}}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}49-20\sqrt{6}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 49- 20 \sqrt{6}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 1 } \cdot \left( 49- 20 \sqrt{6}\right) = \color{blue}{1} \cdot49+\color{blue}{1} \cdot- 20 \sqrt{6} = \\ = 49- 20 \sqrt{6} $$ Simplify denominator. $$ \color{blue}{ \left( 49 + 20 \sqrt{6}\right) } \cdot \left( 49- 20 \sqrt{6}\right) = \color{blue}{49} \cdot49+\color{blue}{49} \cdot- 20 \sqrt{6}+\color{blue}{ 20 \sqrt{6}} \cdot49+\color{blue}{ 20 \sqrt{6}} \cdot- 20 \sqrt{6} = \\ = 2401- 980 \sqrt{6} + 980 \sqrt{6}-2400 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Remove 1 from denominator. |
This page was created using
Rationalize Denominator Calculator