Answer
$$\frac{-4}{\sqrt{10}}=-\frac{2\sqrt{10}}{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{-4}{\sqrt{10}}& \xlongequal{ }-\frac{4}{\sqrt{10}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}- \, \frac{ 4 }{\sqrt{ 10 }} \times \frac{ \color{orangered}{\sqrt{ 10 }} }{ \color{orangered}{\sqrt{ 10 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-\frac{4\sqrt{10}}{10} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}- \, \frac{ 4 \sqrt{ 10 } : \color{blue}{ 2 } }{ 10 : \color{blue}{ 2 } } \xlongequal{ } \\[1 em] & \xlongequal{ }-\frac{2\sqrt{10}}{5}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 10 }}$. |
| ② | In denominator we have $ \sqrt{ 10 } \cdot \sqrt{ 10 } = 10 $. |
| ③ | Divide both the top and bottom numbers by $ \color{blue}{ 2 }$. |
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