Question
Answer
$$\dfrac{2}{\sqrt{21}+\sqrt{15}}=\dfrac{\sqrt{21}-\sqrt{15}}{3}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2}{\sqrt{21}+\sqrt{15}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2}{\sqrt{21}+\sqrt{15}}\frac{\sqrt{21}-\sqrt{15}}{\sqrt{21}-\sqrt{15}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{2\sqrt{21}-2\sqrt{15}}{21-3\sqrt{35}+3\sqrt{35}-15} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{2\sqrt{21}-2\sqrt{15}}{6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{\sqrt{21}-\sqrt{15}}{3}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{21}- \sqrt{15}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 2 } \cdot \left( \sqrt{21}- \sqrt{15}\right) = \color{blue}{2} \cdot \sqrt{21}+\color{blue}{2} \cdot- \sqrt{15} = \\ = 2 \sqrt{21}- 2 \sqrt{15} $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{21} + \sqrt{15}\right) } \cdot \left( \sqrt{21}- \sqrt{15}\right) = \color{blue}{ \sqrt{21}} \cdot \sqrt{21}+\color{blue}{ \sqrt{21}} \cdot- \sqrt{15}+\color{blue}{ \sqrt{15}} \cdot \sqrt{21}+\color{blue}{ \sqrt{15}} \cdot- \sqrt{15} = \\ = 21- 3 \sqrt{35} + 3 \sqrt{35}-15 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Divide both numerator and denominator by 2. |
This page was created using
Rationalize Denominator Calculator