Question
Answer
$$\dfrac{2^7\sqrt{7}}{2\sqrt{7}}=64$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2^7\sqrt{7}}{2\sqrt{7}}& \xlongequal{ }\frac{128\sqrt{7}}{2\sqrt{7}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{128\sqrt{7}}{2\sqrt{7}}\frac{\sqrt{7}}{\sqrt{7}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{896}{14} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 896 : \color{orangered}{ 14 } }{ 14 : \color{orangered}{ 14 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{64}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}64\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{7}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 128 \sqrt{7} } \cdot \sqrt{7} = 896 $$ Simplify denominator. $$ \color{blue}{ 2 \sqrt{7} } \cdot \sqrt{7} = 14 $$ |
| ③ | Divide both the top and bottom numbers by $ \color{orangered}{ 14 } $. |
| ④ | Remove 1 from denominator. |
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