Question
Answer
$$\dfrac{2\sqrt{10}}{\sqrt{82}}=\dfrac{2\sqrt{205}}{41}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2\sqrt{10}}{\sqrt{82}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2\sqrt{10}}{\sqrt{82}}\frac{\sqrt{82}}{\sqrt{82}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{4\sqrt{205}}{82} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 4 \sqrt{ 205 } : \color{blue}{ 2 } } { 82 : \color{blue}{ 2 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{2\sqrt{205}}{41}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{82}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 2 \sqrt{10} } \cdot \sqrt{82} = 4 \sqrt{205} $$ Simplify denominator. $$ \color{blue}{ \sqrt{82} } \cdot \sqrt{82} = 82 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 2 } $. |
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