Answer
$$\frac{4\sqrt{5}}{5\sqrt{10}}=\frac{2\sqrt{2}}{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{4\sqrt{5}}{5\sqrt{10}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{4\sqrt{5}}{5\sqrt{10}}\frac{\sqrt{10}}{\sqrt{10}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{20\sqrt{2}}{50} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 20 \sqrt{ 2 } : \color{blue}{ 10 } } { 50 : \color{blue}{ 10 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{2\sqrt{2}}{5}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{10}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 4 \sqrt{5} } \cdot \sqrt{10} = 20 \sqrt{2} $$ Simplify denominator. $$ \color{blue}{ 5 \sqrt{10} } \cdot \sqrt{10} = 50 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 10 } $. |
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