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

Responses

81−−√<9

81−−√>9

71 −−−√<61−−√

71−−√>61−−√

1 answer

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:

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