Question

Using rational approximations, what is an inequality statement comparing 21−−√ and 17−−√
? Enter <, >, or =.(1 point)
The inequality is: 21−−√ (response area) 17−−√.

Answer 1

To compare \( \sqrt{21} \) and \( \sqrt{17} \) using rational approximations, we can calculate the approximate values of each square root.

- The square root of 21 can be approximated as follows:
\[
\sqrt{21} \approx 4.58 \quad (\text{since } 4.58^2 = 20.9764 \text{ and } 4.59^2 = 20.0881)
\]

- The square root of 17 can be approximated similarly:
\[
\sqrt{17} \approx 4.12 \quad (\text{since } 4.12^2 = 16.9744 \text{ and } 4.13^2 = 17.0569)
\]

Now, comparing these two values:
\[
4.58 > 4.12
\]

Therefore, we can conclude:
\[
\sqrt{21} > \sqrt{17}
\]

The inequality is:
\[
\sqrt{21} > \sqrt{17}
\]

So the final statement is:
\[
\sqrt{21} > \sqrt{17}
\]