Question
Answer
$$\dfrac{8}{\sqrt{7}+\sqrt{10}}=\dfrac{-8\sqrt{7}+8\sqrt{10}}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{8}{\sqrt{7}+\sqrt{10}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{8}{\sqrt{7}+\sqrt{10}}\frac{\sqrt{7}-\sqrt{10}}{\sqrt{7}-\sqrt{10}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{8\sqrt{7}-8\sqrt{10}}{7-\sqrt{70}+\sqrt{70}-10} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{8\sqrt{7}-8\sqrt{10}}{-3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-8\sqrt{7}+8\sqrt{10}}{3}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{7}- \sqrt{10}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 8 } \cdot \left( \sqrt{7}- \sqrt{10}\right) = \color{blue}{8} \cdot \sqrt{7}+\color{blue}{8} \cdot- \sqrt{10} = \\ = 8 \sqrt{7}- 8 \sqrt{10} $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{7} + \sqrt{10}\right) } \cdot \left( \sqrt{7}- \sqrt{10}\right) = \color{blue}{ \sqrt{7}} \cdot \sqrt{7}+\color{blue}{ \sqrt{7}} \cdot- \sqrt{10}+\color{blue}{ \sqrt{10}} \cdot \sqrt{7}+\color{blue}{ \sqrt{10}} \cdot- \sqrt{10} = \\ = 7- \sqrt{70} + \sqrt{70}-10 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Multiply both numerator and denominator by -1. |
This page was created using
Rationalize Denominator Calculator