Question

Approximate Values of Irrational Numbers Quick Check
3 of 53 of 5 Items
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

Answer 1

To determine which statements about the square roots are true, let's evaluate each one:

1. **\(\sqrt{48} > \sqrt{36}\)**:
- \(\sqrt{36} = 6\)
- \(\sqrt{48} \approx 6.93\) (since \(48\) is between \(36\) and \(64\))
- This statement is **true**.

2. **\(\sqrt{48} < \sqrt{36}\)**:
- This is the opposite of the first statement, which we found to be true, so this is **false**.

3. **\(\sqrt{49} < 7\)**:
- \(\sqrt{49} = 7\)
- Therefore, this statement is **false**.

4. **\(\sqrt{49} > 7\)**:
- Similarly, this is the opposite of the third statement, so this is also **false**.

Based on this evaluation, the **true** statement is:

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