Question

Using rational approximations, what statement is true?

√81 > 9

√71 > √ 61

√81 <9

√71 < √61

Answer 1

To evaluate the statements provided, let's analyze each one:

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

2. **√71 > √61**:
To compare these two square roots, we can take the squares of both sides:
\[
71 > 61
\]
This statement is true.

3. **√81 < 9**:
Again, since \( \sqrt{81} = 9 \), this statement is false.

4. **√71 < √61**:
As previously noted, since \( 71 > 61 \), this makes the statement false.

Thus, the only true statement is:
**√71 > √61**.