Using rational approximations, what statement is true?

Question

√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.