Using rational approximations, what statement is true?(1 point)

Question

Responses

81−−√>9
start root 81 end root greater than 9

71−−√>61−−√
start root 71 end root greater than start root 61 end root

71 −−−√<61−−√
start root 71 end root less than start root 61 end root

81−−√<9
start root 81 end root less than 9

Answer 1

To evaluate the provided statements using rational approximations, we can calculate the square roots involved.

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

   • This means \( \sqrt{81} < 9 \) is false.
   • Therefore, \( \sqrt{81} > 9 \) is also false.

2. For \( \sqrt{71} \) and \( \sqrt{61} \):

   • Approximating these values, we find:
     • \( \sqrt{71} \approx 8.43 \)
     • \( \sqrt{61} \approx 7.81 \)
   • Since \( 8.43 > 7.81 \), we have \( \sqrt{71} > \sqrt{61} \) is true.

3. Therefore, \( \sqrt{71} < \sqrt{61} \) is false.

4. In summary, the true statement among the options is:

   • \( \sqrt{71} > \sqrt{61} \)

Thus, the correct response is: \( \sqrt{71} > \sqrt{61} \)