Question
Answer
$$\dfrac{\sqrt{14}}{5\sqrt{2}-6}=\dfrac{5\sqrt{7}+3\sqrt{14}}{7}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{14}}{5\sqrt{2}-6}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{14}}{5\sqrt{2}-6}\frac{5\sqrt{2}+6}{5\sqrt{2}+6} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{10\sqrt{7}+6\sqrt{14}}{50+30\sqrt{2}-30\sqrt{2}-36} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{10\sqrt{7}+6\sqrt{14}}{14} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{5\sqrt{7}+3\sqrt{14}}{7}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 5 \sqrt{2} + 6} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \sqrt{14} } \cdot \left( 5 \sqrt{2} + 6\right) = \color{blue}{ \sqrt{14}} \cdot 5 \sqrt{2}+\color{blue}{ \sqrt{14}} \cdot6 = \\ = 10 \sqrt{7} + 6 \sqrt{14} $$ Simplify denominator. $$ \color{blue}{ \left( 5 \sqrt{2}-6\right) } \cdot \left( 5 \sqrt{2} + 6\right) = \color{blue}{ 5 \sqrt{2}} \cdot 5 \sqrt{2}+\color{blue}{ 5 \sqrt{2}} \cdot6\color{blue}{-6} \cdot 5 \sqrt{2}\color{blue}{-6} \cdot6 = \\ = 50 + 30 \sqrt{2}- 30 \sqrt{2}-36 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Divide both numerator and denominator by 2. |
This page was created using
Rationalize Denominator Calculator