Question
Answer
$$\dfrac{\sqrt{39}}{2\sqrt{39}}=\dfrac{1}{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{39}}{2\sqrt{39}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{39}}{2\sqrt{39}}\frac{\sqrt{39}}{\sqrt{39}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{39}{78} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 39 : \color{orangered}{ 39 } }{ 78 : \color{orangered}{ 39 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{1}{2}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{39}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \sqrt{39} } \cdot \sqrt{39} = 39 $$ Simplify denominator. $$ \color{blue}{ 2 \sqrt{39} } \cdot \sqrt{39} = 78 $$ |
| ③ | Divide both the top and bottom numbers by $ \color{orangered}{ 39 } $. |
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