Question

Using rational approximations, what statement is true?(1 point)
Responses

π<9–√π<9–√

π>9–√pi is greater than square root of 9

3>9–√3 is greater than square root of 9

3<9–√3<9–√

Answer 1

To determine the truth of the statements provided with rational approximations, we can calculate the approximate values of π and the square root of 9.

1. **Calculating the values:**
- π (approximately) = 3.14
- \(\sqrt{9} = 3\)

Now, we can analyze each of the statements based on these approximate values:

1. **π < 9 - √π < 9 - √**
- Since \(\sqrt{9} = 3\), this expression would mean \(\pi < 3 < 9\), which is false because π is approximately 3.14.

2. **π > 9 - √**
- This is essentially saying π > 3. Since π is approximately 3.14, this statement is true.

3. **3 > 9 - √3**
- This statement is comparing 3 to \(\sqrt{9} = 3\). This is false as well, because 3 is not greater than 3.

4. **3 < 9 - √3 < 9 - √**
- This is saying \(3 < 3 < 3\), which is also false.

Based on the analysis, the only true statement is:

**π > 9 - √** (π is greater than the square root of 9).