Question
Answer
$$\dfrac{\sqrt{15}-1}{2\sqrt{15}+4\sqrt{2}}=\dfrac{15-2\sqrt{30}-\sqrt{15}+2\sqrt{2}}{14}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{15}-1}{2\sqrt{15}+4\sqrt{2}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{15}-1}{2\sqrt{15}+4\sqrt{2}}\frac{2\sqrt{15}-4\sqrt{2}}{2\sqrt{15}-4\sqrt{2}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{30-4\sqrt{30}-2\sqrt{15}+4\sqrt{2}}{60-8\sqrt{30}+8\sqrt{30}-32} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{30-4\sqrt{30}-2\sqrt{15}+4\sqrt{2}}{28} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{15-2\sqrt{30}-\sqrt{15}+2\sqrt{2}}{14}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 2 \sqrt{15}- 4 \sqrt{2}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( \sqrt{15}-1\right) } \cdot \left( 2 \sqrt{15}- 4 \sqrt{2}\right) = \color{blue}{ \sqrt{15}} \cdot 2 \sqrt{15}+\color{blue}{ \sqrt{15}} \cdot- 4 \sqrt{2}\color{blue}{-1} \cdot 2 \sqrt{15}\color{blue}{-1} \cdot- 4 \sqrt{2} = \\ = 30- 4 \sqrt{30}- 2 \sqrt{15} + 4 \sqrt{2} $$ Simplify denominator. $$ \color{blue}{ \left( 2 \sqrt{15} + 4 \sqrt{2}\right) } \cdot \left( 2 \sqrt{15}- 4 \sqrt{2}\right) = \color{blue}{ 2 \sqrt{15}} \cdot 2 \sqrt{15}+\color{blue}{ 2 \sqrt{15}} \cdot- 4 \sqrt{2}+\color{blue}{ 4 \sqrt{2}} \cdot 2 \sqrt{15}+\color{blue}{ 4 \sqrt{2}} \cdot- 4 \sqrt{2} = \\ = 60- 8 \sqrt{30} + 8 \sqrt{30}-32 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Divide both numerator and denominator by 2. |
This page was created using
Rationalize Denominator Calculator