Using rational approximations, what statement is true?(1 point) Responses 81−−√<9 start root 81 end root less than 9 71−−√>61−−√ start root 71 end root greater than start root 61 end root 81−−√>9 start root 81 end root greater than 9 71 −−−√<61−−√

Answer 1

To analyze which statement is true using rational approximations, let's evaluate each expression.

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

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

2. \( \sqrt{71} > \sqrt{61} \)

   • We know that \( 71 > 61 \), and since the square root function is increasing for positive numbers, \( \sqrt{71} > \sqrt{61} \) is true.

3. \( \sqrt{81} > 9 \)

   • Again, \( \sqrt{81} = 9 \), so this statement is false since \( 9 = 9 \).

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

   • This statement is false, as established in the second point.

Based on the evaluations above, the true statement among the given options is:

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