Question
Answer
$$\dfrac{\sqrt{7}-1}{2\sqrt{14}}=\dfrac{7\sqrt{2}-\sqrt{14}}{28}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{7}-1}{2\sqrt{14}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{7}-1}{2\sqrt{14}}\frac{\sqrt{14}}{\sqrt{14}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{7\sqrt{2}-\sqrt{14}}{28}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{14}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( \sqrt{7}-1\right) } \cdot \sqrt{14} = \color{blue}{ \sqrt{7}} \cdot \sqrt{14}\color{blue}{-1} \cdot \sqrt{14} = \\ = 7 \sqrt{2}- \sqrt{14} $$ Simplify denominator. $$ \color{blue}{ 2 \sqrt{14} } \cdot \sqrt{14} = 28 $$ |
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