Question

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

48−−√>36−−√
start root 48 end root greater than start root 36 end root

48−−√<36−−√
start root 48 end root less than start root 36 end root

49−−√<7
start root 49 end root less than 7

49−−√>7
start root 49 end root greater than 7

Answer 1

To determine which statements are true, let's calculate the square roots and compare them:

1. **For \(\sqrt{48}\) and \(\sqrt{36}\)**:
- \(\sqrt{36} = 6\)
- \(\sqrt{48} \approx 6.928\) (since \(48\) is between \(36\) and \(49\))
- Therefore, \(\sqrt{48} > \sqrt{36}\).

2. **For \(\sqrt{49}\)**:
- \(\sqrt{49} = 7\)
- The statement \(\sqrt{49} < 7\) is false.
- The statement \(\sqrt{49} > 7\) is also false.

Based on the calculations, the correct statement is:

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

So, the true statement is:

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