Answer
$$\frac{11+4\sqrt{2}}{2\sqrt{19}}=\frac{11\sqrt{19}+4\sqrt{38}}{38}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{11+4\sqrt{2}}{2\sqrt{19}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{11+4\sqrt{2}}{2\sqrt{19}}\frac{\sqrt{19}}{\sqrt{19}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{11\sqrt{19}+4\sqrt{38}}{38}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{19}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 11 + 4 \sqrt{2}\right) } \cdot \sqrt{19} = \color{blue}{11} \cdot \sqrt{19}+\color{blue}{ 4 \sqrt{2}} \cdot \sqrt{19} = \\ = 11 \sqrt{19} + 4 \sqrt{38} $$ Simplify denominator. $$ \color{blue}{ 2 \sqrt{19} } \cdot \sqrt{19} = 38 $$ |
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