Question
Answer
$$\dfrac{12}{5-\sqrt{9}}=6$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{12}{5-\sqrt{9}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{12}{5-\sqrt{9}}\frac{5+\sqrt{9}}{5+\sqrt{9}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{60+36}{25+15-15-9} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{96}{16} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 96 : \color{orangered}{ 16 } }{ 16 : \color{orangered}{ 16 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{6}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}6\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 5 + \sqrt{9}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 12 } \cdot \left( 5 + \sqrt{9}\right) = \color{blue}{12} \cdot5+\color{blue}{12} \cdot \sqrt{9} = \\ = 60 + 36 $$ Simplify denominator. $$ \color{blue}{ \left( 5- \sqrt{9}\right) } \cdot \left( 5 + \sqrt{9}\right) = \color{blue}{5} \cdot5+\color{blue}{5} \cdot \sqrt{9}\color{blue}{- \sqrt{9}} \cdot5\color{blue}{- \sqrt{9}} \cdot \sqrt{9} = \\ = 25 + 15-15-9 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Divide both the top and bottom numbers by $ \color{orangered}{ 16 } $. |
| ⑤ | Remove 1 from denominator. |
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