Question
Answer
$$\dfrac{-1-9\sqrt{7}}{\sqrt{38}}=\dfrac{-\sqrt{38}-9\sqrt{266}}{38}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{-1-9\sqrt{7}}{\sqrt{38}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{-1-9\sqrt{7}}{\sqrt{38}}\frac{\sqrt{38}}{\sqrt{38}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{-\sqrt{38}-9\sqrt{266}}{38}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{38}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( -1- 9 \sqrt{7}\right) } \cdot \sqrt{38} = \color{blue}{-1} \cdot \sqrt{38}\color{blue}{- 9 \sqrt{7}} \cdot \sqrt{38} = \\ = - \sqrt{38}- 9 \sqrt{266} $$ Simplify denominator. $$ \color{blue}{ \sqrt{38} } \cdot \sqrt{38} = 38 $$ |
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