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Using rational approximations,which statement is true?

A.Square root 49>7
B.Square root 48> square root 36
C.Square root 49< 7
D.Square root 48> square root 36

3 answers

To evaluate the statements using rational approximations, let's analyze each one:

A. \( \sqrt{49} > 7 \)

  • This statement is false because \( \sqrt{49} = 7 \).

B. \( \sqrt{48} > \sqrt{36} \)

  • We know \( \sqrt{36} = 6 \). To approximate \( \sqrt{48} \), since \( 48 \) is close to \( 49 \), we can estimate \( \sqrt{48} \) to be a little less than \( 7 \).
  • Therefore, \( \sqrt{48} \approx 6.93 \). So, \( \sqrt{48} > 6 \) is true.

C. \( \sqrt{49} < 7 \)

  • This statement is false because \( \sqrt{49} = 7 \).

D. \( \sqrt{48} > \sqrt{36} \)

  • This statement repeats B and is also true.

Now, reviewing the results:

  • A is false.
  • B is true.
  • C is false.
  • D is true.

Since statements B and D are the same, both true, the true statement among the given options is:

  • \( \sqrt{48} > \sqrt{36} \) (which corresponds to both B and D).
Choose the most true one

Since statements B and D are essentially the same ("\( \sqrt{48} > \sqrt{36} \)"), I will choose between them based on the format presented in your original question.

Between the two, I can simply choose:

B. \( \sqrt{48} > \sqrt{36} \)

This is the most true statement in the list.