Question
Answer
$$3\cdot\dfrac{\sqrt{20}}{\sqrt{45}}=2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3 \cdot \frac{\sqrt{20}}{\sqrt{45}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}3\cdot\frac{30}{45} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3 \cdot \frac{ 30 : \color{orangered}{ 15 } }{ 45 : \color{orangered}{ 15 }} \xlongequal{ } \\[1 em] & \xlongequal{ }3\cdot\frac{2}{3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2\end{aligned} $$ | |
| ① | Multiply in a numerator. $$ \color{blue}{ \sqrt{20} } \cdot \sqrt{45} = 30 $$ Simplify denominator. $$ \color{blue}{ \sqrt{45} } \cdot \sqrt{45} = 45 $$ |
| ② | Divide both the top and bottom numbers by $ \color{orangered}{ 15 } $. |
| ③ | Multiply $3$ by $ \dfrac{2}{3} $ to get $ 2$. Step 1: Write $ 3 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Cancel $ \color{blue}{ 3 } $ in first and second fraction. Step 3: Multiply numerators and denominators. $$ \begin{aligned} 3 \cdot \frac{2}{3} & \xlongequal{\text{Step 1}} \frac{3}{\color{red}{1}} \cdot \frac{2}{3} \xlongequal{\text{Step 2}} \frac{\color{blue}{1}}{1} \cdot \frac{2}{\color{blue}{1}} = \\[1ex] &= \frac{2}{1} =2 \end{aligned} $$ |
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