If a number is subtracted from the square of its one - half, the result is 48. The square root of the numbers is

If a number is subtracted from the square of its one-half, the result is 48.

Mathematically, let the number be x:

((x/2))² - x = 48

Simplify and rearrange:

x²/4 - x = 48
x² - 4x - 192 = 0

Solving the quadratic equation using the quadratic formula:

x = [4 ± √(16 + 768)] / 2 = [4 ± 28] / 2

Two possible solutions:

• x = (4 + 28) / 2 = 16
• x = (4 - 28) / 2 = -12

Square roots of the solutions:

• √16 = 4 (valid root)
• √-12 = Not a real number

Answer: The square root of the number is 4.