Question

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

Your sure?

Answer 2

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:

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