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