using ratinoal approximations, what statement is true?

Question

48−−√ < 36−−√
49−−√ < 7
49−−√ > 7
48 −−√ ? 36−−√

Answer 1

To evaluate the statements using rational approximations:

1. \( \sqrt{48} < \sqrt{36} \):

   • \( \sqrt{48} \approx 6.93 \)
   • \( \sqrt{36} = 6 \)
   • Therefore, this statement is false.

2. \( \sqrt{49} < 7 \):

   • \( \sqrt{49} = 7 \)
   • Therefore, this statement is false.

3. \( \sqrt{49} > 7 \):

   • As established, \( \sqrt{49} = 7 \).
   • Therefore, this statement is false.

4. \( \sqrt{48} ? \sqrt{36} \):

   • Since \( \sqrt{48} \approx 6.93 \) and \( \sqrt{36} = 6 \), we find that \( \sqrt{48} > \sqrt{36} \). Thus, we can express this as \( \sqrt{48} > \sqrt{36} \).

In conclusion:

• \( \sqrt{48} > \sqrt{36} \) is the only true statement.