Question
Answer
$$\dfrac{26}{6+\sqrt{10}}=6-\sqrt{10}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{26}{6+\sqrt{10}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{26}{6+\sqrt{10}}\frac{6-\sqrt{10}}{6-\sqrt{10}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{156-26\sqrt{10}}{36-6\sqrt{10}+6\sqrt{10}-10} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{156-26\sqrt{10}}{26} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{6-\sqrt{10}}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}6-\sqrt{10}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 6- \sqrt{10}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 26 } \cdot \left( 6- \sqrt{10}\right) = \color{blue}{26} \cdot6+\color{blue}{26} \cdot- \sqrt{10} = \\ = 156- 26 \sqrt{10} $$ Simplify denominator. $$ \color{blue}{ \left( 6 + \sqrt{10}\right) } \cdot \left( 6- \sqrt{10}\right) = \color{blue}{6} \cdot6+\color{blue}{6} \cdot- \sqrt{10}+\color{blue}{ \sqrt{10}} \cdot6+\color{blue}{ \sqrt{10}} \cdot- \sqrt{10} = \\ = 36- 6 \sqrt{10} + 6 \sqrt{10}-10 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Divide both numerator and denominator by 26. |
| ⑤ | Remove 1 from denominator. |
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