Question
Answer
$$\dfrac{4-\sqrt{5}}{2\sqrt{14}}=\dfrac{4\sqrt{14}-\sqrt{70}}{28}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{4-\sqrt{5}}{2\sqrt{14}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{4-\sqrt{5}}{2\sqrt{14}}\frac{\sqrt{14}}{\sqrt{14}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{4\sqrt{14}-\sqrt{70}}{28}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{14}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 4- \sqrt{5}\right) } \cdot \sqrt{14} = \color{blue}{4} \cdot \sqrt{14}\color{blue}{- \sqrt{5}} \cdot \sqrt{14} = \\ = 4 \sqrt{14}- \sqrt{70} $$ Simplify denominator. $$ \color{blue}{ 2 \sqrt{14} } \cdot \sqrt{14} = 28 $$ |
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