using ratinoal approximations, what statement is true?

Question

81−−√ < 9
81−−√ > 9
71−−√ > 61−−√
71−−√ < 61−−√

Answer 1

To analyze the statements using rational approximations, let’s evaluate each expression.

1. \(\sqrt{81} < 9\):
   \(\sqrt{81} = 9\)
   Therefore, this statement is false.

2. \(\sqrt{81} > 9\):
   Again, \(\sqrt{81} = 9\)
   Therefore, this statement is false.

3. \(\sqrt{71} > \sqrt{61}\):
   To compare, we need to approximate:

   • \(\sqrt{71} \approx 8.426\)
   • \(\sqrt{61} \approx 7.810\) Since \(8.426 > 7.810\), this statement is true.

4. \(\sqrt{71} < \sqrt{61}\):
   Since we established that \(\sqrt{71} > \sqrt{61}\), this statement is false.

So, the only true statement is:
\(\sqrt{71} > \sqrt{61}\).