Question
Answer
$$\dfrac{16}{\sqrt{41}-25}=-\dfrac{16\sqrt{41}+400}{584}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{16}{\sqrt{41}-25}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{16}{\sqrt{41}-25}\frac{\sqrt{41}+25}{\sqrt{41}+25} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{16\sqrt{41}+400}{41+25\sqrt{41}-25\sqrt{41}-625} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{16\sqrt{41}+400}{-584} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-\frac{16\sqrt{41}+400}{584}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{41} + 25} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 16 } \cdot \left( \sqrt{41} + 25\right) = \color{blue}{16} \cdot \sqrt{41}+\color{blue}{16} \cdot25 = \\ = 16 \sqrt{41} + 400 $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{41}-25\right) } \cdot \left( \sqrt{41} + 25\right) = \color{blue}{ \sqrt{41}} \cdot \sqrt{41}+\color{blue}{ \sqrt{41}} \cdot25\color{blue}{-25} \cdot \sqrt{41}\color{blue}{-25} \cdot25 = \\ = 41 + 25 \sqrt{41}- 25 \sqrt{41}-625 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Place a negative sign in front of a fraction. |
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