Question
Answer
$$10\cdot\dfrac{\sqrt{6}}{\sqrt{24}}=5$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}10 \cdot \frac{\sqrt{6}}{\sqrt{24}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}10\cdot\frac{12}{24} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}10 \cdot \frac{ 12 : \color{orangered}{ 12 } }{ 24 : \color{orangered}{ 12 }} \xlongequal{ } \\[1 em] & \xlongequal{ }10\cdot\frac{1}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}5\end{aligned} $$ | |
| ① | Multiply in a numerator. $$ \color{blue}{ \sqrt{6} } \cdot \sqrt{24} = 12 $$ Simplify denominator. $$ \color{blue}{ \sqrt{24} } \cdot \sqrt{24} = 24 $$ |
| ② | Divide both the top and bottom numbers by $ \color{orangered}{ 12 } $. |
| ③ | Multiply $10$ by $ \dfrac{1}{2} $ to get $ 5$. Write $ 10 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Cancel down by $ \color{blue}{2} $ $$ \begin{aligned} 10 \cdot \frac{1}{2} & = \frac{10}{\color{red}{1}} \cdot \frac{1}{2} = \frac{10 : \color{blue}{2}}{2 : \color{blue}{2}} = \\[1ex] &= \frac{5}{1} =5 \end{aligned} $$ |
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