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

Question

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

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

81−−√>9

Answer 1

To evaluate which statement is true, let's analyze each one:

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

2. \(\sqrt{71} > \sqrt{61}\)
   Since 71 > 61, then \(\sqrt{71} > \sqrt{61}\).
   This statement is true.

3. \(\sqrt{71} < \sqrt{61}\)
   This statement is false, as already determined in the previous step.

4. \(\sqrt{81} > 9\)
   Again, \(\sqrt{81} = 9\).
   This statement is false.

Therefore, the true statement is \(\sqrt{71} > \sqrt{61}\).