Answer
$$\frac{\sqrt{32}+\sqrt{2}}{\sqrt{8}}=\frac{5}{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{32}+\sqrt{2}}{\sqrt{8}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{32}+\sqrt{2}}{\sqrt{8}}\frac{\sqrt{8}}{\sqrt{8}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{16+4}{8} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{20}{8} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 20 : \color{orangered}{ 4 } }{ 8 : \color{orangered}{ 4 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{5}{2}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{8}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( \sqrt{32} + \sqrt{2}\right) } \cdot \sqrt{8} = \color{blue}{ \sqrt{32}} \cdot \sqrt{8}+\color{blue}{ \sqrt{2}} \cdot \sqrt{8} = \\ = 16 + 4 $$ Simplify denominator. $$ \color{blue}{ \sqrt{8} } \cdot \sqrt{8} = 8 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Divide both the top and bottom numbers by $ \color{orangered}{ 4 } $. |
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