Question

Using rational approximations, what statement is true?

A. √12 > pi
B.√16 > 4
C.√12 < pi
D.√16 < 4

Answer 1

To evaluate the statements, we will calculate the values of each expression.

1. **For statement A: \( \sqrt{12} > \pi \)**
We can approximate \( \sqrt{12} \) as follows:
\( \sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3} \).
\( \sqrt{3} \) is approximately \( 1.732 \), so:
\( 2\sqrt{3} \approx 2 \times 1.732 \approx 3.464 \).
We know that \( \pi \) is approximately \( 3.14159 \).
Hence, \( 3.464 > 3.14159 \) → \( \sqrt{12} > \pi \) is **true**.

2. **For statement B: \( \sqrt{16} > 4 \)**
Here, \( \sqrt{16} = 4 \).
So, \( 4 > 4 \) is **false**.

3. **For statement C: \( \sqrt{12} < \pi \)**
Since we determined that \( \sqrt{12} > \pi \) is **true**, this statement is **false**.

4. **For statement D: \( \sqrt{16} < 4 \)**
Again, since \( \sqrt{16} = 4 \), the statement \( 4 < 4 \) is **false**.

Thus, the only statement that is true is **A: \( \sqrt{12} > \pi \)**.