Question
Answer
$$\dfrac{26+6\sqrt{7}}{6+2\sqrt{7}}=9-2\sqrt{7}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{26+6\sqrt{7}}{6+2\sqrt{7}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{26+6\sqrt{7}}{6+2\sqrt{7}}\frac{6-2\sqrt{7}}{6-2\sqrt{7}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{156-52\sqrt{7}+36\sqrt{7}-84}{36-12\sqrt{7}+12\sqrt{7}-28} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{72-16\sqrt{7}}{8} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{9-2\sqrt{7}}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}9-2\sqrt{7}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 6- 2 \sqrt{7}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 26 + 6 \sqrt{7}\right) } \cdot \left( 6- 2 \sqrt{7}\right) = \color{blue}{26} \cdot6+\color{blue}{26} \cdot- 2 \sqrt{7}+\color{blue}{ 6 \sqrt{7}} \cdot6+\color{blue}{ 6 \sqrt{7}} \cdot- 2 \sqrt{7} = \\ = 156- 52 \sqrt{7} + 36 \sqrt{7}-84 $$ Simplify denominator. $$ \color{blue}{ \left( 6 + 2 \sqrt{7}\right) } \cdot \left( 6- 2 \sqrt{7}\right) = \color{blue}{6} \cdot6+\color{blue}{6} \cdot- 2 \sqrt{7}+\color{blue}{ 2 \sqrt{7}} \cdot6+\color{blue}{ 2 \sqrt{7}} \cdot- 2 \sqrt{7} = \\ = 36- 12 \sqrt{7} + 12 \sqrt{7}-28 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Divide both numerator and denominator by 8. |
| ⑤ | Remove 1 from denominator. |
This page was created using
Rationalize Denominator Calculator