Estimate \( \sqrt{50} \) to the hundredths place. 1. Estimate between two whole numbers: \( 7^{2}=49,8^{2}=64 \) 2. Estimate further to the tenths place: \( 7.0^{2}=49.0,7.1^{2}=50.41 \) 3. Estimate further to the hundredths place: The \( \sqrt{50} \) is between

1. We know that \[ 7^2 = 49 \quad \text{and} \quad 8^2 = 64, \] so \[ \sqrt{50} \text{ is between } 7 \text{ and } 8. \] 2. Checking at the tenths place, consider: \[ 7.0^2 = 49.00 \quad \text{and} \quad 7.1^2 = 50.41. \] Since \[ 50 \text{ lies between } 49.00 \text{ and } 50.41, \] it follows that \[ \sqrt{50} \text{ is between } 7.0 \text{ and } 7.1. \] 3. To estimate to the hundredths place, we try a value between 7.0 and 7.1. A common estimate is \( 7.07 \). Checking this value: \[ 7.07^2 \approx 49.9849, \] which is very close to 50. For comparison, \[ 7.08^2 \approx 50.1264. \] Since \( 50 \) is very nearly reached at \( 7.07 \), when rounding to the hundredths place we have \[ \sqrt{50} \approx 7.07. \]