Using rational approximations, what statement is true? (1 point)

71 >
−− √ 61
−− √
81 < 9
−− √
81 > 9
−− √
71 <
−− √ 61

1 answer

To evaluate the given statements, let's find the rational approximations for each square root:

  1. For \( \sqrt{61} \):

    • \( \sqrt{61} \) is approximately 7.81 (since \( 7.8^2 = 60.84 \) and \( 7.9^2 = 62.41 \)).
  2. For \( \sqrt{81} \):

    • \( \sqrt{81} = 9 \).

Now let's analyze the statements:

  1. \( 71 > \sqrt{61} \):

    • Since \( \sqrt{61} \approx 7.81 \), this statement is true since \( 71 > 7.81 \).
  2. \( 81 < 9 \):

    • This statement is false as \( 81 > 9 \).
  3. \( 81 > 9 \):

    • This is true because \( 81 > 9 \).
  4. \( 71 < \sqrt{61} \):

    • This is false since \( 71 > 7.81 \).

Based on this analysis, the true statements are:

  • \( 71 > \sqrt{61} \)
  • \( 81 > 9 \)

Since you need one statement that is true, both \( 71 > \sqrt{61} \) and \( 81 > 9 \) are valid, but just pick one of them based on your requirement of 1 point. The statement "71 > √61" is true.