Question

Using rational approximations, what statement is true?(1 point)
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:
- \( \sqrt{71} > \sqrt{61} \)