Answer
$$\frac{7\sqrt{3}}{\sqrt{18}}=\frac{7\sqrt{6}}{6}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{7\sqrt{3}}{\sqrt{18}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{7\sqrt{3}}{\sqrt{18}}\frac{\sqrt{18}}{\sqrt{18}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{21\sqrt{6}}{18} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{ 21 \sqrt{ 6 } : \color{blue}{ 3 } } { 18 : \color{blue}{ 3 }} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{7\sqrt{6}}{6}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ \sqrt{18}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 7 \sqrt{3} } \cdot \sqrt{18} = 21 \sqrt{6} $$ Simplify denominator. $$ \color{blue}{ \sqrt{18} } \cdot \sqrt{18} = 18 $$ |
| ③ | Divide numerator and denominator by $ \color{blue}{ 3 } $. |
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