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

Question

Responses

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

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

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

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

Answer 1

To evaluate the statements using rational approximations, let's calculate the relevant square roots:

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

   • So, \( \sqrt{81} > 9 \) is false and \( \sqrt{81} < 9 \) is also false.

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

   • Approximate values:
     • \( \sqrt{71} \approx 8.426 \)
     • \( \sqrt{61} \approx 7.810 \)
   • Now comparing:
     • \( \sqrt{71} < \sqrt{61} \) is false.
     • \( \sqrt{71} > \sqrt{61} \) is true.

The correct statement is:

• \( \sqrt{71} > \sqrt{61} \)