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

Question

Responses

49−−√<7

48−−√<36−−√

49−−√>7

48−−√>36−−√

Answer 1

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:

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