Question
Answer
$$\dfrac{3}{8\sqrt{7}-\sqrt{35}}=\dfrac{24\sqrt{7}+3\sqrt{35}}{413}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{3}{8\sqrt{7}-\sqrt{35}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{3}{8\sqrt{7}-\sqrt{35}}\frac{8\sqrt{7}+\sqrt{35}}{8\sqrt{7}+\sqrt{35}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{24\sqrt{7}+3\sqrt{35}}{448+56\sqrt{5}-56\sqrt{5}-35} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{24\sqrt{7}+3\sqrt{35}}{413}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 8 \sqrt{7} + \sqrt{35}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 3 } \cdot \left( 8 \sqrt{7} + \sqrt{35}\right) = \color{blue}{3} \cdot 8 \sqrt{7}+\color{blue}{3} \cdot \sqrt{35} = \\ = 24 \sqrt{7} + 3 \sqrt{35} $$ Simplify denominator. $$ \color{blue}{ \left( 8 \sqrt{7}- \sqrt{35}\right) } \cdot \left( 8 \sqrt{7} + \sqrt{35}\right) = \color{blue}{ 8 \sqrt{7}} \cdot 8 \sqrt{7}+\color{blue}{ 8 \sqrt{7}} \cdot \sqrt{35}\color{blue}{- \sqrt{35}} \cdot 8 \sqrt{7}\color{blue}{- \sqrt{35}} \cdot \sqrt{35} = \\ = 448 + 56 \sqrt{5}- 56 \sqrt{5}-35 $$ |
| ③ | Simplify numerator and denominator |
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