Question
Answer
$$\dfrac{15}{2\sqrt{3}+5\sqrt{2}}=\dfrac{-30\sqrt{3}+75\sqrt{2}}{38}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{15}{2\sqrt{3}+5\sqrt{2}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{15}{2\sqrt{3}+5\sqrt{2}}\frac{2\sqrt{3}-5\sqrt{2}}{2\sqrt{3}-5\sqrt{2}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{30\sqrt{3}-75\sqrt{2}}{12-10\sqrt{6}+10\sqrt{6}-50} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{30\sqrt{3}-75\sqrt{2}}{-38} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-30\sqrt{3}+75\sqrt{2}}{38}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 2 \sqrt{3}- 5 \sqrt{2}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 15 } \cdot \left( 2 \sqrt{3}- 5 \sqrt{2}\right) = \color{blue}{15} \cdot 2 \sqrt{3}+\color{blue}{15} \cdot- 5 \sqrt{2} = \\ = 30 \sqrt{3}- 75 \sqrt{2} $$ Simplify denominator. $$ \color{blue}{ \left( 2 \sqrt{3} + 5 \sqrt{2}\right) } \cdot \left( 2 \sqrt{3}- 5 \sqrt{2}\right) = \color{blue}{ 2 \sqrt{3}} \cdot 2 \sqrt{3}+\color{blue}{ 2 \sqrt{3}} \cdot- 5 \sqrt{2}+\color{blue}{ 5 \sqrt{2}} \cdot 2 \sqrt{3}+\color{blue}{ 5 \sqrt{2}} \cdot- 5 \sqrt{2} = \\ = 12- 10 \sqrt{6} + 10 \sqrt{6}-50 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Multiply both numerator and denominator by -1. |
This page was created using
Rationalize Denominator Calculator