Question
Answer
$$\dfrac{6+\sqrt{9}}{\sqrt{9}}=3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{6+\sqrt{9}}{\sqrt{9}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{6+\sqrt{9}}{\sqrt{9}}\frac{\sqrt{9}}{\sqrt{9}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{18+9}{9} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{27}{9} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 27 : \color{orangered}{ 9 } }{ 9 : \color{orangered}{ 9 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{3}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}3\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{9}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 6 + \sqrt{9}\right) } \cdot \sqrt{9} = \color{blue}{6} \cdot \sqrt{9}+\color{blue}{ \sqrt{9}} \cdot \sqrt{9} = \\ = 18 + 9 $$ Simplify denominator. $$ \color{blue}{ \sqrt{9} } \cdot \sqrt{9} = 9 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Divide both the top and bottom numbers by $ \color{orangered}{ 9 } $. |
| ⑤ | Remove 1 from denominator. |
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