Question
Answer
$$\dfrac{\sqrt{7}}{4-\sqrt{2}}=\dfrac{4\sqrt{7}+\sqrt{14}}{14}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\sqrt{7}}{4-\sqrt{2}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\sqrt{7}}{4-\sqrt{2}}\frac{4+\sqrt{2}}{4+\sqrt{2}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{4\sqrt{7}+\sqrt{14}}{16+4\sqrt{2}-4\sqrt{2}-2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{4\sqrt{7}+\sqrt{14}}{14}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 4 + \sqrt{2}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \sqrt{7} } \cdot \left( 4 + \sqrt{2}\right) = \color{blue}{ \sqrt{7}} \cdot4+\color{blue}{ \sqrt{7}} \cdot \sqrt{2} = \\ = 4 \sqrt{7} + \sqrt{14} $$ Simplify denominator. $$ \color{blue}{ \left( 4- \sqrt{2}\right) } \cdot \left( 4 + \sqrt{2}\right) = \color{blue}{4} \cdot4+\color{blue}{4} \cdot \sqrt{2}\color{blue}{- \sqrt{2}} \cdot4\color{blue}{- \sqrt{2}} \cdot \sqrt{2} = \\ = 16 + 4 \sqrt{2}- 4 \sqrt{2}-2 $$ |
| ③ | Simplify numerator and denominator |
This page was created using
Rationalize Denominator Calculator