Answer
$$\frac{4\sqrt{2}}{\sqrt{10}}=\frac{4\sqrt{5}}{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{4\sqrt{2}}{\sqrt{10}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{4\sqrt{2}}{\sqrt{10}}\frac{\sqrt{10}}{\sqrt{10}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{8\sqrt{5}}{10} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 8 \sqrt{ 5 } : \color{blue}{ 2 } } { 10 : \color{blue}{ 2 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{4\sqrt{5}}{5}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{10}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 4 \sqrt{2} } \cdot \sqrt{10} = 8 \sqrt{5} $$ Simplify denominator. $$ \color{blue}{ \sqrt{10} } \cdot \sqrt{10} = 10 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 2 } $. |
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