Answer
$$\frac{\sqrt{41}+\sqrt{29}}{\sqrt{41}\cdot\sqrt{29}}=\frac{41\sqrt{29}+29\sqrt{41}}{1189}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{41}+\sqrt{29}}{\sqrt{41}\cdot\sqrt{29}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{41}+\sqrt{29}}{\sqrt{41}\cdot\sqrt{29}}\frac{\sqrt{1189}}{\sqrt{1189}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{41\sqrt{29}+29\sqrt{41}}{1189}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{1189}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( \sqrt{41} + \sqrt{29}\right) } \cdot \sqrt{1189} = \color{blue}{ \sqrt{41}} \cdot \sqrt{1189}+\color{blue}{ \sqrt{29}} \cdot \sqrt{1189} = \\ = 41 \sqrt{29} + 29 \sqrt{41} $$ Simplify denominator. $$ \color{blue}{ \sqrt{1189} } \cdot \sqrt{1189} = 1189 $$ |
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