Answer
$$\frac{16\sqrt{47}}{8\sqrt{141}}=\frac{2\sqrt{3}}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{16\sqrt{47}}{8\sqrt{141}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{16\sqrt{47}}{8\sqrt{141}}\frac{\sqrt{141}}{\sqrt{141}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{752\sqrt{3}}{1128} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 752 \sqrt{ 3 } : \color{blue}{ 376 } } { 1128 : \color{blue}{ 376 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{2\sqrt{3}}{3}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{141}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 16 \sqrt{47} } \cdot \sqrt{141} = 752 \sqrt{3} $$ Simplify denominator. $$ \color{blue}{ 8 \sqrt{141} } \cdot \sqrt{141} = 1128 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 376 } $. |
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