Answer
$$\frac{10+\sqrt{5}}{4\sqrt{5}}=\frac{2\sqrt{5}+1}{4}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{10+\sqrt{5}}{4\sqrt{5}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{10+\sqrt{5}}{4\sqrt{5}}\frac{\sqrt{5}}{\sqrt{5}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{10\sqrt{5}+5}{20} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{2\sqrt{5}+1}{4}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{5}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 10 + \sqrt{5}\right) } \cdot \sqrt{5} = \color{blue}{10} \cdot \sqrt{5}+\color{blue}{ \sqrt{5}} \cdot \sqrt{5} = \\ = 10 \sqrt{5} + 5 $$ Simplify denominator. $$ \color{blue}{ 4 \sqrt{5} } \cdot \sqrt{5} = 20 $$ |
| ③ | Divide both numerator and denominator by 5. |
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