Question
Answer
$$\dfrac{14+3\sqrt{7}}{\sqrt{7}}=2\sqrt{7}+3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{14+3\sqrt{7}}{\sqrt{7}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{14+3\sqrt{7}}{\sqrt{7}}\frac{\sqrt{7}}{\sqrt{7}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{14\sqrt{7}+21}{7} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{2\sqrt{7}+3}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2\sqrt{7}+3\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{7}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 14 + 3 \sqrt{7}\right) } \cdot \sqrt{7} = \color{blue}{14} \cdot \sqrt{7}+\color{blue}{ 3 \sqrt{7}} \cdot \sqrt{7} = \\ = 14 \sqrt{7} + 21 $$ Simplify denominator. $$ \color{blue}{ \sqrt{7} } \cdot \sqrt{7} = 7 $$ |
| ③ | Divide both numerator and denominator by 7. |
| ④ | Remove 1 from denominator. |
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