Answer
$$\frac{21}{\sqrt{448}}=\frac{3\sqrt{7}}{8}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{21}{\sqrt{448}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}} \frac{ 21 }{\sqrt{ 448 }} \times \frac{ \color{orangered}{\sqrt{ 448 }} }{ \color{orangered}{\sqrt{ 448 }}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{21\sqrt{448}}{448} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}} \frac{ 21 \sqrt{ 64 \cdot 7 }}{ 448 } \xlongequal{ } \\[1 em] & \xlongequal{ } \frac{ 21 \cdot 8 \sqrt{ 7 } }{ 448 } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{168\sqrt{7}}{448} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}} \frac{ 168 \sqrt{ 7 } : \color{blue}{ 56 } }{ 448 : \color{blue}{ 56 } } \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{3\sqrt{7}}{8}\end{aligned} $$ | |
| ① | Multiply both top and bottom by $ \color{orangered}{ \sqrt{ 448 }}$. |
| ② | In denominator we have $ \sqrt{ 448 } \cdot \sqrt{ 448 } = 448 $. |
| ③ | Simplify $ \sqrt{ 448 } $. |
| ④ | Divide both the top and bottom numbers by $ \color{blue}{ 56 }$. |
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