Question
Answer
$$\dfrac{5}{10+\sqrt{17}}=\dfrac{50-5\sqrt{17}}{83}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{5}{10+\sqrt{17}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5}{10+\sqrt{17}}\frac{10-\sqrt{17}}{10-\sqrt{17}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{50-5\sqrt{17}}{100-10\sqrt{17}+10\sqrt{17}-17} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{50-5\sqrt{17}}{83}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 10- \sqrt{17}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 5 } \cdot \left( 10- \sqrt{17}\right) = \color{blue}{5} \cdot10+\color{blue}{5} \cdot- \sqrt{17} = \\ = 50- 5 \sqrt{17} $$ Simplify denominator. $$ \color{blue}{ \left( 10 + \sqrt{17}\right) } \cdot \left( 10- \sqrt{17}\right) = \color{blue}{10} \cdot10+\color{blue}{10} \cdot- \sqrt{17}+\color{blue}{ \sqrt{17}} \cdot10+\color{blue}{ \sqrt{17}} \cdot- \sqrt{17} = \\ = 100- 10 \sqrt{17} + 10 \sqrt{17}-17 $$ |
| ③ | Simplify numerator and denominator |
This page was created using
Rationalize Denominator Calculator