Answer
$$\frac{\sqrt{2}}{\sqrt{2}}\cdot5=5$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{2}}{\sqrt{2}}\cdot5& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2}{2}\cdot5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{ 2 : \color{orangered}{ 2 } }{ 2 : \color{orangered}{ 2 }} \cdot 5 \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{1}{1}\cdot5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}1\cdot5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}5\end{aligned} $$ | |
| ① | Multiply in a numerator. $$ \color{blue}{ \sqrt{2} } \cdot \sqrt{2} = 2 $$ Simplify denominator. $$ \color{blue}{ \sqrt{2} } \cdot \sqrt{2} = 2 $$ |
| ② | Divide both the top and bottom numbers by $ \color{orangered}{ 2 } $. |
| ③ | Remove 1 from denominator. |
| ④ | $ 1 \cdot 5 = 5 $ |
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Simplify Radical Expression