Question
Answer
$$\dfrac{4\sqrt{7}+7\sqrt{2}}{\sqrt{14}}=2\sqrt{2}+\sqrt{7}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{4\sqrt{7}+7\sqrt{2}}{\sqrt{14}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{4\sqrt{7}+7\sqrt{2}}{\sqrt{14}}\frac{\sqrt{14}}{\sqrt{14}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{28\sqrt{2}+14\sqrt{7}}{14} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{2\sqrt{2}+\sqrt{7}}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2\sqrt{2}+\sqrt{7}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{14}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 4 \sqrt{7} + 7 \sqrt{2}\right) } \cdot \sqrt{14} = \color{blue}{ 4 \sqrt{7}} \cdot \sqrt{14}+\color{blue}{ 7 \sqrt{2}} \cdot \sqrt{14} = \\ = 28 \sqrt{2} + 14 \sqrt{7} $$ Simplify denominator. $$ \color{blue}{ \sqrt{14} } \cdot \sqrt{14} = 14 $$ |
| ③ | Divide both numerator and denominator by 14. |
| ④ | Remove 1 from denominator. |
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