Question
Answer
$$\dfrac{2\sqrt{123}}{4\sqrt{41}}=\dfrac{\sqrt{3}}{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2\sqrt{123}}{4\sqrt{41}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2\sqrt{123}}{4\sqrt{41}}\frac{\sqrt{41}}{\sqrt{41}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{82\sqrt{3}}{164} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\sqrt{3}}{2}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{41}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 2 \sqrt{123} } \cdot \sqrt{41} = 82 \sqrt{3} $$ Simplify denominator. $$ \color{blue}{ 4 \sqrt{41} } \cdot \sqrt{41} = 164 $$ |
| ③ | Divide both numerator and denominator by 82. |
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