Question
Answer
$$\dfrac{7\sqrt{6}+\sqrt{24}}{\sqrt{6}}=9$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{7\sqrt{6}+\sqrt{24}}{\sqrt{6}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{7\sqrt{6}+\sqrt{24}}{\sqrt{6}}\frac{\sqrt{6}}{\sqrt{6}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{42+12}{6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{54}{6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 54 : \color{orangered}{ 6 } }{ 6 : \color{orangered}{ 6 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{9}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}9\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{6}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 7 \sqrt{6} + \sqrt{24}\right) } \cdot \sqrt{6} = \color{blue}{ 7 \sqrt{6}} \cdot \sqrt{6}+\color{blue}{ \sqrt{24}} \cdot \sqrt{6} = \\ = 42 + 12 $$ Simplify denominator. $$ \color{blue}{ \sqrt{6} } \cdot \sqrt{6} = 6 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Divide both the top and bottom numbers by $ \color{orangered}{ 6 } $. |
| ⑤ | Remove 1 from denominator. |
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