Answer
$$\frac{4\sqrt{2205}}{21\sqrt{5}}=4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{4\sqrt{2205}}{21\sqrt{5}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{4\sqrt{2205}}{21\sqrt{5}}\frac{\sqrt{5}}{\sqrt{5}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{420}{105} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 420 : \color{orangered}{ 105 } }{ 105 : \color{orangered}{ 105 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{4}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}4\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{5}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 4 \sqrt{2205} } \cdot \sqrt{5} = 420 $$ Simplify denominator. $$ \color{blue}{ 21 \sqrt{5} } \cdot \sqrt{5} = 105 $$ |
| ③ | Divide both the top and bottom numbers by $ \color{orangered}{ 105 } $. |
| ④ | Remove 1 from denominator. |
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