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