Using rational approximations, what statement is true?(1 point)

Question

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 evaluate the statements, let's calculate the square roots of 71, 61, and 81 and compare their values:

1. Calculating square roots:

   • \(\sqrt{71} \approx 8.426\)
   • \(\sqrt{61} \approx 7.810\)
   • \(\sqrt{81} = 9\)

2. Comparing the values:

   • \(\sqrt{71} > \sqrt{61}\) (approximately \(8.426 > 7.810\))
   • \(\sqrt{71} < \sqrt{61}\) (this is false)
   • \(\sqrt{81} > 9\) (this is false)
   • \(\sqrt{81} < 9\) (this is also false)

Thus, the only true statement is:

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

So the correct choice is:

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