Answer
$$\frac{5\sqrt{21}}{7\sqrt{70}}=\frac{\sqrt{30}}{14}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{5\sqrt{21}}{7\sqrt{70}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{5\sqrt{21}}{7\sqrt{70}}\frac{\sqrt{70}}{\sqrt{70}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{35\sqrt{30}}{490} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\sqrt{30}}{14}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{70}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 5 \sqrt{21} } \cdot \sqrt{70} = 35 \sqrt{30} $$ Simplify denominator. $$ \color{blue}{ 7 \sqrt{70} } \cdot \sqrt{70} = 490 $$ |
| ③ | Divide both numerator and denominator by 35. |
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