Question
Answer
$$\dfrac{5}{3+5\sqrt{90}}=\dfrac{-15+75\sqrt{10}}{2241}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{5}{3+5\sqrt{90}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5}{3+5\sqrt{90}}\frac{3-5\sqrt{90}}{3-5\sqrt{90}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{15-75\sqrt{10}}{9-45\sqrt{10}+45\sqrt{10}-2250} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{15-75\sqrt{10}}{-2241} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-15+75\sqrt{10}}{2241}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 3- 5 \sqrt{90}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 5 } \cdot \left( 3- 5 \sqrt{90}\right) = \color{blue}{5} \cdot3+\color{blue}{5} \cdot- 5 \sqrt{90} = \\ = 15- 75 \sqrt{10} $$ Simplify denominator. $$ \color{blue}{ \left( 3 + 5 \sqrt{90}\right) } \cdot \left( 3- 5 \sqrt{90}\right) = \color{blue}{3} \cdot3+\color{blue}{3} \cdot- 5 \sqrt{90}+\color{blue}{ 5 \sqrt{90}} \cdot3+\color{blue}{ 5 \sqrt{90}} \cdot- 5 \sqrt{90} = \\ = 9- 45 \sqrt{10} + 45 \sqrt{10}-2250 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Multiply both numerator and denominator by -1. |
This page was created using
Rationalize Denominator Calculator