Answer
$$\frac{\sqrt{2}}{\sqrt{40}}=\frac{\sqrt{5}}{10}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{2}}{\sqrt{40}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{2}}{\sqrt{40}}\frac{\sqrt{40}}{\sqrt{40}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{4\sqrt{5}}{40} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\sqrt{5}}{10}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{40}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \sqrt{2} } \cdot \sqrt{40} = 4 \sqrt{5} $$ Simplify denominator. $$ \color{blue}{ \sqrt{40} } \cdot \sqrt{40} = 40 $$ |
| ③ | Divide both numerator and denominator by 4. |
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