Question

Using rational approximations, what statement is true?
A. √48 ≤ 7
B. √ 49 ≥ 7
C. √ 48 ≤ √36
D. √ 48 ≥ √ 36

Answer 1

To evaluate the statements using rational approximations, we first need to calculate the values of the square roots involved.

1. **Calculate \( \sqrt{48} \)**:
\[
\sqrt{48} = \sqrt{16 \times 3} = 4\sqrt{3} \approx 4 \times 1.732 = 6.928 \text{ (approx)}
\]

2. **Calculate \( \sqrt{49} \)**:
\[
\sqrt{49} = 7
\]

3. **Calculate \( \sqrt{36} \)**:
\[
\sqrt{36} = 6
\]

Now, we will evaluate each of the statements:

**A. \( \sqrt{48} \leq 7 \)**
From our approximation, \( 6.928 \leq 7 \) is true.

**B. \( \sqrt{49} \geq 7 \)**
Since \( \sqrt{49} = 7 \), it is also true that \( 7 \geq 7 \).

**C. \( \sqrt{48} \leq \sqrt{36} \)**
From our calculations, \( 6.928 \leq 6 \) is false.

**D. \( \sqrt{48} \geq \sqrt{36} \)**
Since \( 6.928 \geq 6 \) is true.

### Summary of Findings:
- Statement A is **true**.
- Statement B is **true**.
- Statement C is **false**.
- Statement D is **true**.

Thus, the true statements are **A**, **B**, and **D**.