Answer
$$\frac{7\sqrt{32}}{5\sqrt{63}}=\frac{4\sqrt{14}}{15}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{7\sqrt{32}}{5\sqrt{63}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{7\sqrt{32}}{5\sqrt{63}}\frac{\sqrt{63}}{\sqrt{63}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{84\sqrt{14}}{315} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 84 \sqrt{ 14 } : \color{blue}{ 21 } } { 315 : \color{blue}{ 21 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{4\sqrt{14}}{15}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{63}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 7 \sqrt{32} } \cdot \sqrt{63} = 84 \sqrt{14} $$ Simplify denominator. $$ \color{blue}{ 5 \sqrt{63} } \cdot \sqrt{63} = 315 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 21 } $. |
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