Answer
$$\frac{5+\sqrt{3}}{\sqrt{8}}=\frac{5\sqrt{2}+\sqrt{6}}{4}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{5+\sqrt{3}}{\sqrt{8}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5+\sqrt{3}}{\sqrt{8}}\frac{\sqrt{8}}{\sqrt{8}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{10\sqrt{2}+2\sqrt{6}}{8} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{5\sqrt{2}+\sqrt{6}}{4}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{8}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 5 + \sqrt{3}\right) } \cdot \sqrt{8} = \color{blue}{5} \cdot \sqrt{8}+\color{blue}{ \sqrt{3}} \cdot \sqrt{8} = \\ = 10 \sqrt{2} + 2 \sqrt{6} $$ Simplify denominator. $$ \color{blue}{ \sqrt{8} } \cdot \sqrt{8} = 8 $$ |
| ③ | Divide both numerator and denominator by 2. |
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