Question

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

12 −−−√ >π
start root 12 end root greater than pi

12 −−−√<π
start root 12 end root less than pi

16 −−−√<4
start root 16 end root less than 4

16−−√>4

Answer 1

To evaluate the statements using rational approximations, we can simplify and compare the values on both sides.

1. **√12 > π**: Let's approximate √12. √12 is approximately 3.464. The value of π is approximately 3.142. So, √12 (≈ 3.464) is indeed greater than π (≈ 3.142). This statement is **true**.

2. **√12 < π**: This is the opposite of the first statement and is therefore **false**.

3. **√16 < 4**: √16 equals 4. Thus, this statement is **false** since they are equal.

4. **√16 > 4**: This is also the opposite of the equality in the previous statement, making it **false**.

Thus, the true statement is: **√12 > π**.