For Problems \( 6-8 \), answer the question and complete the statement. 6. Is \( \sqrt{14} \) between 3.0 and 3.5 or 3.5 and 4.0 ?

To determine whether \( \sqrt{14} \) is between 3.0 and 3.5 or between 3.5 and 4.0, we can calculate the square of the numbers in these ranges and compare them to 14. 1. Calculate \( 3.0^2 \) and \( 3.5^2 \): \[ 3.0^2 = 9.0 \] \[ 3.5^2 = 12.25 \] 2. Calculate \( 3.5^2 \) and \( 4.0^2 \): \[ 4.0^2 = 16.0 \] Now we can summarize the results: - \( 3.0^2 = 9.0 < 14 \) - \( 3.5^2 = 12.25 < 14 \) - \( 4.0^2 = 16.0 > 14 \) Since \( 14 \) is greater than \( 12.25 \) and less than \( 16.0 \), we conclude that: \[ \sqrt{14} \text{ is between } 3.5 \text{ and } 4.0. \] Thus, the complete statement is: **\( \sqrt{14} \) is between 3.5 and 4.0.**