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 less than start root 61 end root

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

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

Answer 1

To evaluate the statements involving square roots and determine which one is true, let's calculate the values of the expressions:

1. \(\sqrt{81}\): \[ \sqrt{81} = 9 \] Therefore, the statement \(\sqrt{81} < 9\) is false, and \(\sqrt{81} > 9\) is also false.

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

   • Approximate values:
     • \(\sqrt{71} \approx 8.426\)
     • \(\sqrt{61} \approx 7.810\)

   So we can examine the statements:

   • \(\sqrt{71} < \sqrt{61}\) is false because \(8.426 > 7.810\).
   • \(\sqrt{71} > \sqrt{61}\) is true.

Thus, the only statement that is true is:

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

Answer 2

Your sure?