Question
Answer
$$5\cdot\dfrac{\sqrt{75}}{4\sqrt{6}}=\dfrac{25\sqrt{2}}{8}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}5 \cdot \frac{\sqrt{75}}{4\sqrt{6}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}5 \cdot \frac{15\sqrt{2}}{24} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{75\sqrt{2}}{24} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 75 \sqrt{ 2 } : \color{blue}{ 3 } } { 24 : \color{blue}{ 3 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{25\sqrt{2}}{8}\end{aligned} $$ | |
| ① | Multiply in a numerator. $$ \color{blue}{ \sqrt{75} } \cdot \sqrt{6} = 15 \sqrt{2} $$ Simplify denominator. $$ \color{blue}{ 4 \sqrt{6} } \cdot \sqrt{6} = 24 $$ |
| ② | $$ \color{blue}{ 5 } \cdot 15 \sqrt{2} = 75 \sqrt{2} $$$$ \color{blue}{ 1 } \cdot 24 = 24 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 3 } $. |
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