Question

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

Answer 1

Let's evaluate each statement using rational approximations and the properties of square roots.

1. **Statement A: \( \sqrt{48} \leq 7 \)**
- Calculating \( \sqrt{48} \):
\[
\sqrt{48} \approx 6.928
\]
- Since \( 6.928 \leq 7 \), this statement is **true**.

2. **Statement B: \( \sqrt{49} \geq 7 \)**
- Calculating \( \sqrt{49} \):
\[
\sqrt{49} = 7
\]
- Since \( 7 \geq 7 \), this statement is also **true**.

3. **Statement C: \( \sqrt{48} \leq \sqrt{36} \)**
- Calculating \( \sqrt{36} \):
\[
\sqrt{36} = 6
\]
- Since \( 6.928 \) (which is \( \sqrt{48} \)) is not less than or equal to \( 6 \), this statement is **false**.

4. **Statement D: \( \sqrt{48} \geq \sqrt{36} \)**
- Given that \( \sqrt{48} \approx 6.928 \) and \( \sqrt{36} = 6 \):
- Since \( 6.928 \geq 6 \), this statement is **true**.

Among the evaluated statements, both A, B, and D turned out to be true. Since the original condition specified that only one can be true, it seems that we misunderstood the requirement.

Given the context of common approximations:
- **Confirming highest accuracy**:
- \( \sqrt{48} \approx 6.928 \)
- \( \sqrt{36} = 6 \)
- \( \sqrt{49} = 7 \)

For clarity:
- **Statement A** is true.
- **Statement B** is true.
- **Statement C** is false.
- **Statement D** is true.

To fit the expectation that only one must be true, I apologize; thus, if strictly one choice is requested, you may want reevaluation based on constraints possibly overlooked.

Given conventional disagreement in this specification and closer examination:
- Considering misorginization, **A and D move in expected correctness while clearly, C fails in continuity against rational approximation.**
- Thus, effectively, presented best choice dependent on inputs - hence **consider A:**
\[
\text{Choose: } A \text{ (√48 ≤ 7)}
\]
As the first-fit under 'less than.'