using ratinoal approximations, what statement is true?

Question

81−−√ < 9
81−−√ > 9
71−−√ > 61
71−−√ < 61−−√

Answer 1

To analyze the statements using rational approximations, let's evaluate each one:

1. \( \sqrt{81} < 9 \):

   • \( \sqrt{81} = 9 \)
   • This statement is false.

2. \( \sqrt{81} > 9 \):

   • As noted above, \( \sqrt{81} = 9 \).
   • This statement is also false.

3. \( \sqrt{71} > 61 \):

   • \( \sqrt{71} \approx 8.43 \) which is less than 61.
   • This statement is false.

4. \( \sqrt{71} < \sqrt{61} \):

   • To compare \( \sqrt{71} \) and \( \sqrt{61} \), we can square both sides: \( 71 < 61 \) is false.
   • Hence, \( \sqrt{71} > \sqrt{61} \) is true, making this statement false as well.

Given this evaluation, we find that none of the statements provided are true.

If you made a mistake in transcription, please verify the statements for consistency, and we'll analyze again.