sing 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

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

71 −−−√<61−−√

Answer 1

To determine which statement is true using rational approximations, let's evaluate each option.

1. \( \sqrt{81} > 9 \):
   \(\sqrt{81} = 9\), so this statement is false.

2. \( \sqrt{71} > \sqrt{61} \):
   To compare, we can square both sides: \( 71 > 61 \) is true. Therefore, \( \sqrt{71} > \sqrt{61} \) is true.

3. \( \sqrt{81} < 9 \):
   \(\sqrt{81} = 9\), so this statement is false.

4. \( \sqrt{71} < \sqrt{61} \):
   From the earlier comparison, since \( 71 > 61 \), this statement is false.

Thus, the true statement is:

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