Using rational approximations, what is an inequality statement comparing 21−−√

Question

and 17−−√
? Enter <, >, or =.(1 point)

Answer 1

To compare \(\sqrt{21}\) and \(\sqrt{17}\), we can use rational approximations or calculate their decimal values directly.

1. Calculate \(\sqrt{21}\) and \(\sqrt{17}\):

   • \(\sqrt{21} \approx 4.582575\)
   • \(\sqrt{17} \approx 4.123105\)

2. Now, comparing the two values:

   • Since \(4.582575 > 4.123105\), we can conclude that \(\sqrt{21} > \sqrt{17}\).

Thus, the inequality statement comparing \(\sqrt{21}\) and \(\sqrt{17}\) is: \[ \sqrt{21} > \sqrt{17} \]

The answer is: \[

\]