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 greater than 7

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

Answer 1

To analyze the statements, we need to calculate the values of the square roots:

1. **√48 > √36**:
- √36 = 6
- To compare √48 to 6, we can approximate √48. We know that √49 = 7 (since 49 is a perfect square) and √36 = 6. Therefore, √48 is between 6 and 7, but closer to 7.
- Since √48 is not clearly greater than zero, we check: 48 < 49 (but greater than 36). Thus, we cannot definitively claim √48 > √36.

2. **√48 < √36**:
- As established before, √36 = 6, and √48 is greater than √36, since 48 is greater than 36. So, this statement is false.

3. **√49 > 7**:
- √49 = 7. Therefore, this statement is false.

4. **√49 < 7**:
- Again, since √49 = 7, this statement is false.

Thus, the true statement among the given options is: **√48 > √36**.