Question
Answer
$$\dfrac{-4+\sqrt{3}}{4\sqrt{9}}=\dfrac{-4+\sqrt{3}}{12}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{-4+\sqrt{3}}{4\sqrt{9}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{-4+\sqrt{3}}{4\sqrt{9}}\frac{\sqrt{9}}{\sqrt{9}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-12+3\sqrt{3}}{36} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{-4+\sqrt{3}}{12}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{9}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( -4 + \sqrt{3}\right) } \cdot \sqrt{9} = \color{blue}{-4} \cdot \sqrt{9}+\color{blue}{ \sqrt{3}} \cdot \sqrt{9} = \\ = -12 + 3 \sqrt{3} $$ Simplify denominator. $$ \color{blue}{ 4 \sqrt{9} } \cdot \sqrt{9} = 36 $$ |
| ③ | Divide both numerator and denominator by 3. |
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