Question

Using rational approximations, what statement is true?
a 81−−√>9
b 71−−√>61−−√
c 71 −−−√<61−−√
d 81−−√<9

Answer 1

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