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

Question

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.