Using rational approximations, what statement is true?(1 point)
Responses
12 −−−√<π
start root 12 end root less than pi
16−−√>4
start root 16 end root greater than 4
16 −−−√<4
start root 16 end root less than 4
12 −−−√ >π
start root 12 end root greater than pi
Using rational approximations, what statement is true?(1 point)
√16 < 4
√12 > π
√12 < π
√16 > 4
To determine which statement is true using rational approximations:
12√ is approximately 3.46, and π is approximately 3.14. Therefore, 12√ is greater than π.
16√ is exactly 4, and 4 is equal to 4. Therefore, 16√ is not greater than 4.
16√ is exactly 4, and 4 is greater than 4. Therefore, 16√ is not less than 4.
12√ is approximately 3.46, and π is approximately 3.14. Therefore, 12√ is greater than π.
Based on the rational approximations, the statement "12√ > π" is true.
To determine which statement is true using rational approximations, we need to approximate the square roots and compare them to the given values.
1. √12 < π (less than pi)
We can approximate √12 as follows:
√12 = √(4 × 3) = 2√3 ≈ 2 × 1.732 ≈ 3.464
The value of π is approximately 3.14159, which is less than 3.464.
Therefore, the statement "√12 < π" is true.
2. √16 > 4 (greater than 4)
We can approximate √16 as follows:
√16 = √(4 × 4) = 4
Since the value of 4 is equal to the given value of 4, the statement "√16 > 4" is true.
3. √16 < 4 (less than 4)
We can approximate √16 as 4, as shown in the previous explanation. Since 4 is equal to the given value of 4, the statement "√16 < 4" is false.
4. √12 > π (greater than pi)
We can approximate √12 as 3.464, as shown in the first explanation. The value of π is approximately 3.14159, which is less than 3.464. Therefore, the statement "√12 > π" is false.
Based on the above explanations, the true statement is: √12 < π