Answer
$$\frac{138}{\sqrt{253}}=\frac{6\sqrt{253}}{11}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{138}{\sqrt{253}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 138 }{\sqrt{ 253 }} \times \frac{ \color{orangered}{\sqrt{ 253 }} }{ \color{orangered}{\sqrt{ 253 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{138\sqrt{253}}{253} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 138 \sqrt{ 253 } : \color{blue}{ 23 } }{ 253 : \color{blue}{ 23 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{6\sqrt{253}}{11}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 253 }}$. |
| ② | In denominator we have $ \sqrt{ 253 } \cdot \sqrt{ 253 } = 253 $. |
| ③ | Divide both the top and bottom numbers by $ \color{blue}{ 23 }$. |
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