To compare \(\sqrt{21}\) and \(\sqrt{17}\), we can use rational approximations of these square roots.
First, let's approximate \(\sqrt{21}\) and \(\sqrt{17}\):
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Estimating \(\sqrt{21}\):
- We know that \(4^2 = 16\) and \(5^2 = 25\), so \(4 < \sqrt{21} < 5\).
- A better approximation can be found by calculating \(\sqrt{21} \approx 4.58\).
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Estimating \(\sqrt{17}\):
- Similarly, \(4^2 = 16\) and \(5^2 = 25\), so \(4 < \sqrt{17} < 5\).
- A better approximation is \(\sqrt{17} \approx 4.12\).
Now we can compare the approximations:
- \(\sqrt{21} \approx 4.58\)
- \(\sqrt{17} \approx 4.12\)
Since \(4.58 > 4.12\), we can conclude that: \[ \sqrt{21} > \sqrt{17} \]
Thus, the inequality statement is: \[ \sqrt{21} > \sqrt{17} \]
In summary, the answer is: \(\sqrt{21} > \sqrt{17}\) or simply enter \(>\).