Using rational approximations, what statement is true?

Question

√81>9
√81<9
√71>√61
√71<√61

Answer 1

To evaluate the statements using rational approximations, let's consider each one:

1. \(\sqrt{81} > 9\):

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

2. \(\sqrt{81} < 9\):

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

3. \(\sqrt{71} > \sqrt{61}\):

   • Since 71 is greater than 61, and the square root function is increasing, this statement is true.

4. \(\sqrt{71} < \sqrt{61}\):

   • As established, \(\sqrt{71} > \sqrt{61}\), so this statement is false.

Therefore, the true statement is:

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