Answer
$$\frac{2\sqrt{8}}{\sqrt{32}}=1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2\sqrt{8}}{\sqrt{32}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2\sqrt{8}}{\sqrt{32}}\frac{\sqrt{32}}{\sqrt{32}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{32}{32} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 32 : \color{orangered}{ 32 } }{ 32 : \color{orangered}{ 32 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{1}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}1\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{32}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 2 \sqrt{8} } \cdot \sqrt{32} = 32 $$ Simplify denominator. $$ \color{blue}{ \sqrt{32} } \cdot \sqrt{32} = 32 $$ |
| ③ | Divide both the top and bottom numbers by $ \color{orangered}{ 32 } $. |
| ④ | Remove 1 from denominator. |
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