Answer
$$\frac{6+\sqrt{3}}{\sqrt{11}}=\frac{6\sqrt{11}+\sqrt{33}}{11}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{6+\sqrt{3}}{\sqrt{11}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{6+\sqrt{3}}{\sqrt{11}}\frac{\sqrt{11}}{\sqrt{11}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{6\sqrt{11}+\sqrt{33}}{11}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{11}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 6 + \sqrt{3}\right) } \cdot \sqrt{11} = \color{blue}{6} \cdot \sqrt{11}+\color{blue}{ \sqrt{3}} \cdot \sqrt{11} = \\ = 6 \sqrt{11} + \sqrt{33} $$ Simplify denominator. $$ \color{blue}{ \sqrt{11} } \cdot \sqrt{11} = 11 $$ |
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