Answer
$$\frac{\sqrt{12}}{\sqrt{156}}=\frac{\sqrt{13}}{13}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{12}}{\sqrt{156}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{12}}{\sqrt{156}}\frac{\sqrt{156}}{\sqrt{156}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{12\sqrt{13}}{156} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\sqrt{13}}{13}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{156}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \sqrt{12} } \cdot \sqrt{156} = 12 \sqrt{13} $$ Simplify denominator. $$ \color{blue}{ \sqrt{156} } \cdot \sqrt{156} = 156 $$ |
| ③ | Divide both numerator and denominator by 12. |
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