Using rational approximations what statement is true?

Question

A. square root 81 > 9
B. square root 71 < square root 61
C. square root 81 < 9
D. square root 71 > square root 61

Answer 1

To evaluate the statements using rational approximations, let's analyze each one:

A. \(\sqrt{81} > 9\)
This statement is false because \(\sqrt{81} = 9\).

B. \(\sqrt{71} < \sqrt{61}\)
This statement is false. Since 71 is greater than 61, \(\sqrt{71}\) will be greater than \(\sqrt{61}\).

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

D. \(\sqrt{71} > \sqrt{61}\)
This statement is true. Since 71 is greater than 61, \(\sqrt{71}\) is indeed greater than \(\sqrt{61}\).

Thus, the true statement is:
D. \(\sqrt{71} > \sqrt{61}\).