Question
Answer
$$\dfrac{5}{2\sqrt{10}-3}=\dfrac{10\sqrt{10}+15}{31}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{5}{2\sqrt{10}-3}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5}{2\sqrt{10}-3}\frac{2\sqrt{10}+3}{2\sqrt{10}+3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{10\sqrt{10}+15}{40+6\sqrt{10}-6\sqrt{10}-9} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{10\sqrt{10}+15}{31}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 2 \sqrt{10} + 3} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 5 } \cdot \left( 2 \sqrt{10} + 3\right) = \color{blue}{5} \cdot 2 \sqrt{10}+\color{blue}{5} \cdot3 = \\ = 10 \sqrt{10} + 15 $$ Simplify denominator. $$ \color{blue}{ \left( 2 \sqrt{10}-3\right) } \cdot \left( 2 \sqrt{10} + 3\right) = \color{blue}{ 2 \sqrt{10}} \cdot 2 \sqrt{10}+\color{blue}{ 2 \sqrt{10}} \cdot3\color{blue}{-3} \cdot 2 \sqrt{10}\color{blue}{-3} \cdot3 = \\ = 40 + 6 \sqrt{10}- 6 \sqrt{10}-9 $$ |
| ③ | Simplify numerator and denominator |
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