The square root of 1824 is approximately which value?

The square root of 1824 is approximately which value?

• A. 42.708
• B. 41.0
• C. 44.2
• D. 40.0

Answer: (A)

Estimating a square root by comparing to nearby perfect squares and using a quick linear approximation around a close value. For 1824, note that 42^2 = 1764 and 43^2 = 1849, so the root lies between 42 and 43. Since 1824 is 60 above 1764 and 25 below 1849, it sits closer to 1849, meaning the root is nearer to 43 than to 42. A fast refinement uses the idea that a small change in x around 42 corresponds to twice that x in the square: Δx ≈ ΔN/(2×42) = 60/84 ≈ 0.714, giving about 42.714. A tiny adjustment brings it to roughly 42.708. So the square root is approximately 42.708.

Estimating a square root by comparing to nearby perfect squares and using a quick linear approximation around a close value.

For 1824, note that 42^2 = 1764 and 43^2 = 1849, so the root lies between 42 and 43. Since 1824 is 60 above 1764 and 25 below 1849, it sits closer to 1849, meaning the root is nearer to 43 than to 42. A fast refinement uses the idea that a small change in x around 42 corresponds to twice that x in the square: Δx ≈ ΔN/(2×42) = 60/84 ≈ 0.714, giving about 42.714. A tiny adjustment brings it to roughly 42.708. So the square root is approximately 42.708.