Question
Answer
$$\dfrac{2\sqrt{7}}{3\sqrt{35}}=\dfrac{2\sqrt{5}}{15}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{2\sqrt{7}}{3\sqrt{35}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2\sqrt{7}}{3\sqrt{35}}\frac{\sqrt{35}}{\sqrt{35}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{14\sqrt{5}}{105} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 14 \sqrt{ 5 } : \color{blue}{ 7 } } { 105 : \color{blue}{ 7 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{2\sqrt{5}}{15}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{35}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 2 \sqrt{7} } \cdot \sqrt{35} = 14 \sqrt{5} $$ Simplify denominator. $$ \color{blue}{ 3 \sqrt{35} } \cdot \sqrt{35} = 105 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 7 } $. |
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