Question

Using rational approximations, what statement is true?(1 point) Responses 71−−√>61−−√ start root 71 end root greater than start root 61 end root 71 −−−√<61−−√ start root 71 end root less than start root 61 end root 81−−√>9 start root 81 end root greater than 9 81−−√<9

Answer 1

To determine which statement is true, we can approximate the values of the square roots involved.

1. For \(\sqrt{71}\) and \(\sqrt{61}\):

   • \(\sqrt{71} \approx 8.426\)
   • \(\sqrt{61} \approx 7.810\)

   Comparison: \(8.426 > 7.810\), so \(\sqrt{71} > \sqrt{61}\).

2. For \(\sqrt{81}\) and \(9\):

   • \(\sqrt{81} = 9\)

   Comparison: \(9 = 9\), so \(\sqrt{81} = 9\).

Based on these calculations, we can conclude:

• True statement: \(\sqrt{71} > \sqrt{61}\)

The correct response is: \(\sqrt{71} > \sqrt{61}\)