Question
Answer
$$\dfrac{-\dfrac{17}{11}}{\sqrt{\dfrac{108}{11}}}=\dfrac{(-\dfrac{102}{121})\sqrt{33}}{\dfrac{108}{11}}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{-\frac{17}{11}}{\sqrt{\frac{108}{11}}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{-\frac{17}{11}}{\sqrt{\frac{108}{11}}}\frac{\sqrt{\frac{108}{11}}}{\sqrt{\frac{108}{11}}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{(-\frac{102}{121})\sqrt{33}}{\frac{108}{11}}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{\frac{ 108 }{ 11 }}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ -\frac{ 17 }{ 11 } } \cdot \sqrt{\frac{ 108 }{ 11 }} = - \frac{ 102 }{ 121 } \sqrt{ 33 } $$ Simplify denominator. $$ \color{blue}{ \sqrt{\frac{ 108 }{ 11 }} } \cdot \sqrt{\frac{ 108 }{ 11 }} = \frac{ 108 }{ 11 } $$ |
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