Answer
$$\frac{7\sqrt{90}}{2\sqrt{70}}=\frac{3\sqrt{7}}{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{7\sqrt{90}}{2\sqrt{70}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{7\sqrt{90}}{2\sqrt{70}}\frac{\sqrt{70}}{\sqrt{70}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{210\sqrt{7}}{140} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 210 \sqrt{ 7 } : \color{blue}{ 70 } } { 140 : \color{blue}{ 70 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{3\sqrt{7}}{2}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{70}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 7 \sqrt{90} } \cdot \sqrt{70} = 210 \sqrt{7} $$ Simplify denominator. $$ \color{blue}{ 2 \sqrt{70} } \cdot \sqrt{70} = 140 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 70 } $. |
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