Question
Answer
$$\dfrac{10\sqrt{39}}{5\sqrt{39}}=2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{10\sqrt{39}}{5\sqrt{39}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{10\sqrt{39}}{5\sqrt{39}}\frac{\sqrt{39}}{\sqrt{39}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{390}{195} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 390 : \color{orangered}{ 195 } }{ 195 : \color{orangered}{ 195 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{2}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{39}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 10 \sqrt{39} } \cdot \sqrt{39} = 390 $$ Simplify denominator. $$ \color{blue}{ 5 \sqrt{39} } \cdot \sqrt{39} = 195 $$ |
| ③ | Divide both the top and bottom numbers by $ \color{orangered}{ 195 } $. |
| ④ | Remove 1 from denominator. |
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