Using rational approximations, what statement is true?

A. √48 ≤ 7
B. √ 49 ≥ 7
C. √ 48 ≤ √36
D. √ 48 ≥ √ 36
only one can be true

1 answer

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.'