Question
Answer
$$\dfrac{23}{\sqrt{27}-\sqrt{26}}=69\sqrt{3}+23\sqrt{26}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{23}{\sqrt{27}-\sqrt{26}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{23}{\sqrt{27}-\sqrt{26}}\frac{\sqrt{27}+\sqrt{26}}{\sqrt{27}+\sqrt{26}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{69\sqrt{3}+23\sqrt{26}}{27+3\sqrt{78}-3\sqrt{78}-26} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{69\sqrt{3}+23\sqrt{26}}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}69\sqrt{3}+23\sqrt{26}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{27} + \sqrt{26}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 23 } \cdot \left( \sqrt{27} + \sqrt{26}\right) = \color{blue}{23} \cdot \sqrt{27}+\color{blue}{23} \cdot \sqrt{26} = \\ = 69 \sqrt{3} + 23 \sqrt{26} $$ Simplify denominator. $$ \color{blue}{ \left( \sqrt{27}- \sqrt{26}\right) } \cdot \left( \sqrt{27} + \sqrt{26}\right) = \color{blue}{ \sqrt{27}} \cdot \sqrt{27}+\color{blue}{ \sqrt{27}} \cdot \sqrt{26}\color{blue}{- \sqrt{26}} \cdot \sqrt{27}\color{blue}{- \sqrt{26}} \cdot \sqrt{26} = \\ = 27 + 3 \sqrt{78}- 3 \sqrt{78}-26 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Remove 1 from denominator. |
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