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Using rational approximations what statement is true?

A: √49 < 7

B: √49 > 7

C: √48 < √36

D: √48 > √36

3 answers

To evaluate the statements using rational approximations:

  1. A: √49 < 7

    • This is false because √49 = 7.

  2. B: √49 > 7

    • This is also false because √49 = 7.

  3. C: √48 < √36

    • Calculating these, √48 is approximately 6.93, and √36 = 6. Thus, this statement is false because 6.93 > 6.

  4. D: √48 > √36

    • As established, √48 ≈ 6.93 and √36 = 6. Hence, this statement is true because 6.93 > 6.

Therefore, the correct statement is:

D: √48 > √36.

using rational approximation what statement is true

A: √81 > 9

B: √81 < 9

C: √71 > √61

D: √71 < √61

Let's evaluate each statement using rational approximations:

  1. A: √81 > 9

    • This is false because √81 = 9.

  2. B: √81 < 9

    • This is also false because √81 = 9.

  3. C: √71 > √61

    • Approximating the square roots:
      • √71 is approximately 8.43.
      • √61 is approximately 7.81.
    • This statement is true because 8.43 > 7.81.

  4. D: √71 < √61

    • This is false as established because 8.43 is not less than 7.81.

The correct statement is:

C: √71 > √61.