Question

Using rational approximations, what statement is true? (1 point)
v81 < 9
181 > 9
• V71 < V61
• V71 > V61

Answer 1

To determine which statements are true using rational approximations, we can evaluate each expression.

1. \( \sqrt{81} < 9 \):
- \( \sqrt{81} = 9 \), therefore this statement is false.

2. \( 181 > 9 \):
- This is clearly true since 181 is a much larger number than 9.

3. \( \sqrt{71} < \sqrt{61} \):
- Taking the squares of both sides, we would compare 71 and 61. Since \( 71 > 61 \), this statement is false.

4. \( \sqrt{71} > \sqrt{61} \):
- Again, taking the squares, \( 71 > 61 \) holds true, therefore this statement is true.

In conclusion, the true statements from the options given are:
- \( 181 > 9 \)
- \( \sqrt{71} > \sqrt{61} \)

So, both of the above statements are true, but if you're limited to choosing one, the more direct comparison would be:
- \( 181 > 9 \) is the simplest and most straightforward true statement.