Question

Using rational approximations, what statement is true?

A. √71 < √61
B.√71 > √61
C.√81 < 9
D.√81 > 9

Answer 1

To determine the correctness of the statements using rational approximations, let's examine each one:

A. \( \sqrt{71} < \sqrt{61} \)
- This is false because both numbers are positive, and 71 is greater than 61, so \( \sqrt{71} > \sqrt{61} \).

B. \( \sqrt{71} > \sqrt{61} \)
- This is true for the same reason as above. Since 71 is greater than 61, \( \sqrt{71} \) is indeed greater than \( \sqrt{61} \).

C. \( \sqrt{81} < 9 \)
- This is false because \( \sqrt{81} = 9 \).

D. \( \sqrt{81} > 9 \)
- This is also false because \( \sqrt{81} = 9 \).

From the evaluations above, the true statement is **B. \( \sqrt{71} > \sqrt{61} \)**.