using rational approximations what statement is true would it be square root of 71 is less than square root of 61 square root of 71 is greater than square root of 61 or would it be square root of 81 is less than nine or would it be square root of 81 is more than nine

Answer 1

To determine which statements are true, let's evaluate each one involving rational approximations.

1. \(\sqrt{71}\) is less than \(\sqrt{61}\):

   • To see if this is true, we compare the numbers: \(\sqrt{71} \approx 8.426\) and \(\sqrt{61} \approx 7.810\).
     • Therefore, \(\sqrt{71} > \sqrt{61}\).

2. \(\sqrt{71}\) is greater than \(\sqrt{61}\):

   • Based on the above calculation, this is true: \(\sqrt{71} > \sqrt{61}\).

3. \(\sqrt{81}\) is less than 9:

   • Since \(\sqrt{81} = 9\), this statement is false.

4. \(\sqrt{81}\) is more than 9:

   • As established, \(\sqrt{81} = 9\), so this statement is also false.

Conclusion:

The true statement is: \(\sqrt{71}\) is greater than \(\sqrt{61}\).