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 49−−√<7 start root 49 end root less than 7 48−−√<36−−√ start root 48 end root less than start root 36 end root 49−−√>7

Answer 1

To determine which of the statements is true using rational approximations, we can evaluate the square roots involved.

1. **Evaluate √48 and √36**:
- √36 = 6 (exact)
- √48 can be approximated as:
- √48 = √(16 * 3) = 4√3
- Since √3 is approximately 1.732, then:
- 4√3 ≈ 4 * 1.732 ≈ 6.928

Therefore, √48 ≈ 6.928, and we have:
- √48 > √36 (6.928 > 6).

2. **Evaluate √49**:
- √49 = 7 (exact).

Now, we compare √49 with 7:
- √49 = 7

3. We can summarize:
- √48 > √36 (True)
- √49 < 7 (False, √49 = 7)
- √48 < √36 (False)
- √49 > 7 (False)

Thus, the only true statement is:

**√48 > √36**.