Question

using rational approximations, which statement is true?
pi > square root of 9
3 > square root of 9
pi < square root of 9
3 < square root of 9

Answer 1

To determine which statement is true using rational approximations, let's evaluate each of the expressions:

1. **\( \pi > \sqrt{9} \)**:
- The value of \( \sqrt{9} \) is 3 (since 3 * 3 = 9).
- The value of \( \pi \) is approximately 3.14.
- Therefore, \( \pi > 3 \) is true.

2. **\( 3 > \sqrt{9} \)**:
- As mentioned earlier, \( \sqrt{9} = 3 \).
- Therefore, \( 3 > 3 \) is false.

3. **\( \pi < \sqrt{9} \)**:
- Since \( \pi \) is approximately 3.14 and \( \sqrt{9} = 3 \), this statement is false as \( 3.14 < 3 \) is not true.

4. **\( 3 < \sqrt{9} \)**:
- Since \( \sqrt{9} = 3 \), we have \( 3 < 3 \), which is false.

Thus, the only true statement among those provided is:

**\( \pi > \sqrt{9} \)**.