Question
Answer
$$\sqrt{\dfrac{25}{7}}=\dfrac{5}{7}\sqrt{7}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{\frac{25}{7}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{1}{7}\sqrt{175} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{5}{7}\sqrt{7}\end{aligned} $$ | |
| ① | $$ \sqrt{ \frac{ 25 }{ 7 } } = \frac{ \sqrt{ 25 } } {\sqrt{ 7 }}
= \frac{ \sqrt{ 25 } } {\sqrt{ 7 }} \cdot \frac{ \sqrt{ 7 } } {\sqrt{ 7 }} = \\
= \frac{ \sqrt{ 175 }} { 7 } = \frac{ 1 }{ 7 } \sqrt{ 175 } $$ |
| ② | $$ \frac{ 1 }{ 7 } \sqrt{ 175 } =
\frac{ 1 }{ 7 } \sqrt{ 5 ^2 \cdot 7 } =
\frac{ 1 }{ 7 } \sqrt{ 5 ^2 } \, \sqrt{ 7 } =
\frac{ 1 }{ 7 } \cdot 5 \sqrt{ 7 } =
\frac{ 5 }{ 7 } \sqrt{ 7 } $$ |
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