Question
Answer
$$\dfrac{5}{3+5\sqrt{3}}=\dfrac{-15+25\sqrt{3}}{66}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{5}{3+5\sqrt{3}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5}{3+5\sqrt{3}}\frac{3-5\sqrt{3}}{3-5\sqrt{3}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{15-25\sqrt{3}}{9-15\sqrt{3}+15\sqrt{3}-75} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{15-25\sqrt{3}}{-66} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-15+25\sqrt{3}}{66}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 3- 5 \sqrt{3}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 5 } \cdot \left( 3- 5 \sqrt{3}\right) = \color{blue}{5} \cdot3+\color{blue}{5} \cdot- 5 \sqrt{3} = \\ = 15- 25 \sqrt{3} $$ Simplify denominator. $$ \color{blue}{ \left( 3 + 5 \sqrt{3}\right) } \cdot \left( 3- 5 \sqrt{3}\right) = \color{blue}{3} \cdot3+\color{blue}{3} \cdot- 5 \sqrt{3}+\color{blue}{ 5 \sqrt{3}} \cdot3+\color{blue}{ 5 \sqrt{3}} \cdot- 5 \sqrt{3} = \\ = 9- 15 \sqrt{3} + 15 \sqrt{3}-75 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Multiply both numerator and denominator by -1. |
This page was created using
Rationalize Denominator Calculator