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

Question

and 17−−√
? Enter <, >, or =.(1 point)
The inequality is: 21−−√___17−−√

Answer 1

To compare \( \sqrt{21} \) and \( \sqrt{17} \) using rational approximations, we can calculate their approximate decimal values:

1. \( \sqrt{21} \approx 4.58 \)
2. \( \sqrt{17} \approx 4.12 \)

Since \( 4.58 > 4.12 \), we can conclude that:

\[ \sqrt{21} > \sqrt{17} \]

Thus, the inequality statement is:

\[ \sqrt{21} > \sqrt{17} \]

So the answer is:

\[ \sqrt{21} , > , \sqrt{17} \]