Ben thinks that \( \sqrt{200} \) is between 14 and 15 . Which statement supports Ben's conclusion?

Ben's conclusion that \( \sqrt{200} \) is between 14 and 15 is supported by comparing the squares of 14 and 15 with 200. Here's the reasoning: 1. **Calculate \( 14^2 \):** \[ 14 \times 14 = 196 \] So, \( 14^2 = 196 \). 2. **Calculate \( 15^2 \):** \[ 15 \times 15 = 225 \] So, \( 15^2 = 225 \). 3. **Compare these squares with 200:** \[ 196 < 200 < 225 \] This means: \[ 14^2 < 200 < 15^2 \] Taking the square root of all parts of the inequality, we get: \[ 14 < \sqrt{200} < 15 \] **Therefore, the statement that supports Ben's conclusion is:** *Since \(14^2 = 196\) and \(15^2 = 225\), and \(196 < 200 < 225\), it follows that \(14 < \sqrt{200} < 15\).*