Using rational approximations, what statement is true?

a 81−−√>9
b 71−−√>61−−√
c 71 −−−√<61−−√
d 81−−√<9

1 answer

To determine which statement is true, we can evaluate or approximate the square roots in each option:

a) \( \sqrt{81} > 9 \)

  • We know \( \sqrt{81} = 9 \), so this statement is false.

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

  • Since 71 is greater than 61, their square roots can be compared. Indeed, \( \sqrt{71} \) is greater than \( \sqrt{61} \). So this statement is true.

c) \( \sqrt{71} < \sqrt{61} \)

  • Since \( \sqrt{71} \) is greater than \( \sqrt{61} \), this statement is false.

d) \( \sqrt{81} < 9 \)

  • As mentioned before, \( \sqrt{81} = 9 \), so this statement is false.

The only true statement is b) \( \sqrt{71} > \sqrt{61} \).