Question
Answer
$$\sqrt{\dfrac{4}{45}}=\dfrac{2}{15}\sqrt{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{\frac{4}{45}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{1}{45}\sqrt{180} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{2}{15}\sqrt{5}\end{aligned} $$ | |
| ① | $$ \sqrt{ \frac{ 4 }{ 45 } } = \frac{ \sqrt{ 4 } } {\sqrt{ 45 }}
= \frac{ \sqrt{ 4 } } {\sqrt{ 45 }} \cdot \frac{ \sqrt{ 45 } } {\sqrt{ 45 }} = \\
= \frac{ \sqrt{ 180 }} { 45 } = \frac{ 1 }{ 45 } \sqrt{ 180 } $$ |
| ② | $$ \frac{ 1 }{ 45 } \sqrt{ 180 } =
\frac{ 1 }{ 45 } \sqrt{ 6 ^2 \cdot 5 } =
\frac{ 1 }{ 45 } \sqrt{ 6 ^2 } \, \sqrt{ 5 } =
\frac{ 1 }{ 45 } \cdot 6 \sqrt{ 5 } =
\frac{ 2 }{ 15 } \sqrt{ 5 } $$ |
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