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

Responses

49−−√<7

48−−√<36−−√

49−−√>7

48−−√>36−−√

1 answer

To evaluate which statement is true using rational approximations, let's approximate the values:

  1. For \( \sqrt{49} < 7 \):

    • We know \( \sqrt{49} = 7 \). Thus, this statement is false.
  2. For \( \sqrt{48} < \sqrt{36} \):

    • \( \sqrt{48} \) is approximately \( 6.93 \) and \( \sqrt{36} = 6 \).
    • So \( \sqrt{48} > \sqrt{36} \), making this statement also false.
  3. For \( \sqrt{49} > 7 \):

    • We already established that \( \sqrt{49} = 7 \). Thus, this statement is false.
  4. For \( \sqrt{48} > \sqrt{36} \):

    • As calculated earlier, \( \sqrt{48} \approx 6.93 \) and \( \sqrt{36} = 6 \), thus \( \sqrt{48} > \sqrt{36} \) is true.

In conclusion, the true statement is:

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