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