Question
Answer
$$\sqrt{\dfrac{13}{200}}=\dfrac{1}{20}\sqrt{26}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{\frac{13}{200}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{1}{200}\sqrt{2600} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{1}{20}\sqrt{26}\end{aligned} $$ | |
| ① | $$ \sqrt{ \frac{ 13 }{ 200 } } = \frac{ \sqrt{ 13 } } {\sqrt{ 200 }}
= \frac{ \sqrt{ 13 } } {\sqrt{ 200 }} \cdot \frac{ \sqrt{ 200 } } {\sqrt{ 200 }} = \\
= \frac{ \sqrt{ 2600 }} { 200 } = \frac{ 1 }{ 200 } \sqrt{ 2600 } $$ |
| ② | $$ \frac{ 1 }{ 200 } \sqrt{ 2600 } =
\frac{ 1 }{ 200 } \sqrt{ 10 ^2 \cdot 26 } =
\frac{ 1 }{ 200 } \sqrt{ 10 ^2 } \, \sqrt{ 26 } =
\frac{ 1 }{ 200 } \cdot 10 \sqrt{ 26 } =
\frac{ 1 }{ 20 } \sqrt{ 26 } $$ |
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