Question
Answer
$$\dfrac{24+\sqrt{6}}{16\sqrt{6}}=\dfrac{4\sqrt{6}+1}{16}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{24+\sqrt{6}}{16\sqrt{6}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{24+\sqrt{6}}{16\sqrt{6}}\frac{\sqrt{6}}{\sqrt{6}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{24\sqrt{6}+6}{96} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{4\sqrt{6}+1}{16}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{6}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 24 + \sqrt{6}\right) } \cdot \sqrt{6} = \color{blue}{24} \cdot \sqrt{6}+\color{blue}{ \sqrt{6}} \cdot \sqrt{6} = \\ = 24 \sqrt{6} + 6 $$ Simplify denominator. $$ \color{blue}{ 16 \sqrt{6} } \cdot \sqrt{6} = 96 $$ |
| ③ | Divide both numerator and denominator by 6. |
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