Question
Answer
$$\dfrac{30}{\sqrt{60}}=\sqrt{15}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{30}{\sqrt{60}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 30 }{\sqrt{ 60 }} \times \frac{ \color{orangered}{\sqrt{ 60 }} }{ \color{orangered}{\sqrt{ 60 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{30\sqrt{60}}{60} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 30 \sqrt{ 4 \cdot 15 }}{ 60 } \xlongequal{ } \\[1 em] & \xlongequal{ } \frac{ 30 \cdot 2 \sqrt{ 15 } }{ 60 } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{60\sqrt{15}}{60} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 60 \sqrt{ 15 } : \color{blue}{ 60 } }{ 60 : \color{blue}{ 60 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{\sqrt{15}}{1} \xlongequal{ } \\[1 em] & \xlongequal{ }\sqrt{15}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 60 }}$. |
| ② | In denominator we have $ \sqrt{ 60 } \cdot \sqrt{ 60 } = 60 $. |
| ③ | Simplify $ \sqrt{ 60 } $. |
| ④ | Divide both the top and bottom numbers by $ \color{blue}{ 60 }$. |
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