Answer
$$\frac{10\sqrt{2}}{\sqrt{8}}=5$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{10\sqrt{2}}{\sqrt{8}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{10\sqrt{2}}{\sqrt{8}}\frac{\sqrt{8}}{\sqrt{8}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{40}{8} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 40 : \color{orangered}{ 8 } }{ 8 : \color{orangered}{ 8 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{5}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}5\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{8}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 10 \sqrt{2} } \cdot \sqrt{8} = 40 $$ Simplify denominator. $$ \color{blue}{ \sqrt{8} } \cdot \sqrt{8} = 8 $$ |
| ③ | Divide both the top and bottom numbers by $ \color{orangered}{ 8 } $. |
| ④ | Remove 1 from denominator. |
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