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

Question

Responses

81−−√<9

81−−√>9

71 −−−√<61−−√

71−−√>61−−√

Answer 1

To evaluate the statements using rational approximations, we first find the square roots of the relevant numbers:

1. For the first statement:

   • \( \sqrt{81} = 9 \)
   • Therefore, \( \sqrt{81} = 9 \) and the statement \( \sqrt{81} < 9 \) is false, while \( \sqrt{81} > 9 \) is also false.

2. For the second statement:

   • \( \sqrt{71} \) is approximately \( 8.426 \)
   • \( \sqrt{61} \) is approximately \( 7.810 \)
   • Therefore, \( \sqrt{71} > \sqrt{61} \) is true, while \( \sqrt{71} < \sqrt{61} \) is false.

From this analysis, the true statement is:

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