Question
Answer
$$\sqrt{\dfrac{75}{20}}=\dfrac{1}{2}\sqrt{15}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{\frac{75}{20}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{1}{4}\sqrt{60} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{1}{2}\sqrt{15}\end{aligned} $$ | |
| ① | $$ \sqrt{ \frac{ 15 }{ 4 } } = \frac{ \sqrt{ 15 } } {\sqrt{ 4 }}
= \frac{ \sqrt{ 15 } } {\sqrt{ 4 }} \cdot \frac{ \sqrt{ 4 } } {\sqrt{ 4 }} = \\
= \frac{ \sqrt{ 60 }} { 4 } = \frac{ 1 }{ 4 } \sqrt{ 60 } $$ |
| ② | $$ \frac{ 1 }{ 4 } \sqrt{ 60 } =
\frac{ 1 }{ 4 } \sqrt{ 2 ^2 \cdot 15 } =
\frac{ 1 }{ 4 } \sqrt{ 2 ^2 } \, \sqrt{ 15 } =
\frac{ 1 }{ 4 } \cdot 2 \sqrt{ 15 } =
\frac{ 1 }{ 2 } \sqrt{ 15 } $$ |
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