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