Question
Answer
$$\sqrt{\dfrac{117}{2}}=\dfrac{3}{2}\sqrt{26}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\sqrt{\frac{117}{2}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{1}{2}\sqrt{234} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{3}{2}\sqrt{26}\end{aligned} $$ | |
| ① | $$ \sqrt{ \frac{ 117 }{ 2 } } = \frac{ \sqrt{ 117 } } {\sqrt{ 2 }}
= \frac{ \sqrt{ 117 } } {\sqrt{ 2 }} \cdot \frac{ \sqrt{ 2 } } {\sqrt{ 2 }} = \\
= \frac{ \sqrt{ 234 }} { 2 } = \frac{ 1 }{ 2 } \sqrt{ 234 } $$ |
| ② | $$ \frac{ 1 }{ 2 } \sqrt{ 234 } =
\frac{ 1 }{ 2 } \sqrt{ 3 ^2 \cdot 26 } =
\frac{ 1 }{ 2 } \sqrt{ 3 ^2 } \, \sqrt{ 26 } =
\frac{ 1 }{ 2 } \cdot 3 \sqrt{ 26 } =
\frac{ 3 }{ 2 } \sqrt{ 26 } $$ |
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