Question
Answer
$$\dfrac{3537+1564\sqrt{2}}{60+13\sqrt{2}}=\dfrac{24508+6837\sqrt{2}}{466}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{3537+1564\sqrt{2}}{60+13\sqrt{2}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{3537+1564\sqrt{2}}{60+13\sqrt{2}}\frac{60-13\sqrt{2}}{60-13\sqrt{2}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{212220-45981\sqrt{2}+93840\sqrt{2}-40664}{3600-780\sqrt{2}+780\sqrt{2}-338} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{171556+47859\sqrt{2}}{3262} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{24508+6837\sqrt{2}}{466}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 60- 13 \sqrt{2}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ \left( 3537 + 1564 \sqrt{2}\right) } \cdot \left( 60- 13 \sqrt{2}\right) = \color{blue}{3537} \cdot60+\color{blue}{3537} \cdot- 13 \sqrt{2}+\color{blue}{ 1564 \sqrt{2}} \cdot60+\color{blue}{ 1564 \sqrt{2}} \cdot- 13 \sqrt{2} = \\ = 212220- 45981 \sqrt{2} + 93840 \sqrt{2}-40664 $$ Simplify denominator. $$ \color{blue}{ \left( 60 + 13 \sqrt{2}\right) } \cdot \left( 60- 13 \sqrt{2}\right) = \color{blue}{60} \cdot60+\color{blue}{60} \cdot- 13 \sqrt{2}+\color{blue}{ 13 \sqrt{2}} \cdot60+\color{blue}{ 13 \sqrt{2}} \cdot- 13 \sqrt{2} = \\ = 3600- 780 \sqrt{2} + 780 \sqrt{2}-338 $$ |
| ③ | Simplify numerator and denominator |
| ④ | Divide both numerator and denominator by 7. |
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