Using rational approximations, what statement is true?
√16 < 4
√16 > 4
√12 < π
√12 > π
√16 = 4, so the statement √16 < 4 is false.
√16 = 4, so the statement √16 > 4 is false.
√12 is approximately 3.464, which is less than π ≈ 3.14159, so the statement √12 < π is true.
√12 is approximately 3.464, which is greater than π ≈ 3.14159, so the statement √12 > π is true.
To determine the true statement using rational approximations, we can compare the given expressions to their respective rational approximations.
√16 can be approximated to 4, since 4² = 16. Therefore, √16 = 4.
Comparing √16 to 4, we find that √16 is equal to 4. Therefore, the statement √16 < 4 is false.
Similarly, √12 can be approximated to 3.46 since 3.46² ≈ 11.9716, which is close to 12. However, π (pi) is approximately 3.14, which is less than 3.46.
Comparing √12 to π, we find that √12 is greater than π. Therefore, the statement √12 > π is true.
In conclusion, the true statement is √12 > π.