Question

Using rational approximations, what statement is true? (1 point)
71 >
−− √ 61
−− √
81 < 9
−− √
81 > 9
−− √
71 <
−− √ 61

Answer 1

To evaluate the given statements, let's find the rational approximations for each square root:

1. **For \( \sqrt{61} \)**:
- \( \sqrt{61} \) is approximately 7.81 (since \( 7.8^2 = 60.84 \) and \( 7.9^2 = 62.41 \)).

2. **For \( \sqrt{81} \)**:
- \( \sqrt{81} = 9 \).

Now let's analyze the statements:

1. **\( 71 > \sqrt{61} \)**:
- Since \( \sqrt{61} \approx 7.81 \), this statement is true since \( 71 > 7.81 \).

2. **\( 81 < 9 \)**:
- This statement is false as \( 81 > 9 \).

3. **\( 81 > 9 \)**:
- This is true because \( 81 > 9 \).

4. **\( 71 < \sqrt{61} \)**:
- This is false since \( 71 > 7.81 \).

Based on this analysis, the true statements are:

- \( 71 > \sqrt{61} \)
- \( 81 > 9 \)

Since you need one statement that is true, both \( 71 > \sqrt{61} \) and \( 81 > 9 \) are valid, but just pick one of them based on your requirement of 1 point. The statement **"71 > √61"** is true.