Question
Answer
$$\sqrt{\dfrac{245}{3}}=\dfrac{7}{3}\sqrt{15}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{\frac{245}{3}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{1}{3}\sqrt{735} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{7}{3}\sqrt{15}\end{aligned} $$ | |
| ① | $$ \sqrt{ \frac{ 245 }{ 3 } } = \frac{ \sqrt{ 245 } } {\sqrt{ 3 }}
= \frac{ \sqrt{ 245 } } {\sqrt{ 3 }} \cdot \frac{ \sqrt{ 3 } } {\sqrt{ 3 }} = \\
= \frac{ \sqrt{ 735 }} { 3 } = \frac{ 1 }{ 3 } \sqrt{ 735 } $$ |
| ② | $$ \frac{ 1 }{ 3 } \sqrt{ 735 } =
\frac{ 1 }{ 3 } \sqrt{ 7 ^2 \cdot 15 } =
\frac{ 1 }{ 3 } \sqrt{ 7 ^2 } \, \sqrt{ 15 } =
\frac{ 1 }{ 3 } \cdot 7 \sqrt{ 15 } =
\frac{ 7 }{ 3 } \sqrt{ 15 } $$ |
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