Question
Answer
$$\sqrt{8}+\dfrac{\sqrt{50}}{\sqrt{2}}=2\sqrt{2}+5$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{8}+\frac{\sqrt{50}}{\sqrt{2}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2\sqrt{2}+\frac{\sqrt{50}}{\sqrt{2}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2\sqrt{2}+\frac{10}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2\sqrt{2} + \frac{ 10 : \color{orangered}{ 2 } }{ 2 : \color{orangered}{ 2 }} \xlongequal{ } \\[1 em] & \xlongequal{ }2\sqrt{2}+\frac{5}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2\sqrt{2}+5\end{aligned} $$ | |
| ① | $$ \sqrt{8} =
\sqrt{ 2 ^2 \cdot 2 } =
\sqrt{ 2 ^2 } \, \sqrt{ 2 } =
2 \sqrt{ 2 }$$ |
| ② | Multiply in a numerator. $$ \color{blue}{ \sqrt{50} } \cdot \sqrt{2} = 10 $$ Simplify denominator. $$ \color{blue}{ \sqrt{2} } \cdot \sqrt{2} = 2 $$ |
| ③ | Divide both the top and bottom numbers by $ \color{orangered}{ 2 } $. |
| ④ | Remove 1 from denominator. |
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