To compare \( \sqrt{21} \) and \( \sqrt{17} \) using rational approximations, we can first find approximate values for each square root.
Calculating the approximate values:
- \( \sqrt{21} \) is approximately \( 4.582 \) (since \( 4.5^2 = 20.25 \) and \( 4.6^2 = 21.16 \)).
- \( \sqrt{17} \) is approximately \( 4.123 \) (since \( 4.1^2 = 16.81 \) and \( 4.2^2 = 17.64 \)).
Now, comparing these values:
- \( 4.582 > 4.123 \).
Therefore, we can conclude that:
\[ \sqrt{21} > \sqrt{17} \]
So the inequality statement is:
\[ \sqrt{21} > \sqrt{17} \]