The square root of 124,992 is which of the following?

The square root of 124,992 is which of the following?

• A. 1118 x 10 to the negative second power
• B. 353.54
• C. 42.0
• D. 15.0

Answer: (B)

Estimating a square root by comparing to nearby perfect squares is the key idea. The number 124,992 lies between 353^2 and 354^2. Specifically, 353^2 = 124,609 and 354^2 = 125,316. So the square root must be between 353 and 354, and since 124,992 is closer to 353^2, the root is just above 353. Using a quick interpolation: the distance from 353^2 to the target is 124,992 − 124,609 = 383, and the distance between the two squares is 125,316 − 124,609 = 707. The fraction is 383/707 ≈ 0.541, giving an estimate of 353 + 0.541 ≈ 353.54. Thus the square root is about 353.54. The other numbers are clearly not close to the correct magnitude (they would correspond to much smaller original numbers), so 353.54 is the best approximation.

Estimating a square root by comparing to nearby perfect squares is the key idea. The number 124,992 lies between 353^2 and 354^2. Specifically, 353^2 = 124,609 and 354^2 = 125,316. So the square root must be between 353 and 354, and since 124,992 is closer to 353^2, the root is just above 353.

Using a quick interpolation: the distance from 353^2 to the target is 124,992 − 124,609 = 383, and the distance between the two squares is 125,316 − 124,609 = 707. The fraction is 383/707 ≈ 0.541, giving an estimate of 353 + 0.541 ≈ 353.54.

Thus the square root is about 353.54. The other numbers are clearly not close to the correct magnitude (they would correspond to much smaller original numbers), so 353.54 is the best approximation.