Squared

"Squared" is a mathematical term used to describe the multiplication of a number or an algebraic expression by itself. The operation is commonly denoted by the superscript 2, as in n², where n is the number or variable being squared. The result of squaring a number is called its square.

Squaring a positive real number always yields a non-negative result. For example, 3² equals 9, and (-4)² equals 16. The process involves multiplying the number by itself: n × n. In algebra, squaring is a fundamental operation used in various mathematical contexts, including quadratic equations, geometry, and calculus.

In geometric terms, the square of a side length corresponds to the area of a square with that side length. For example, if the side of a square is length s, then its area is s². This relationship highlights the significance of squaring in measurements of area and spatial relationships.

Squaring has notable properties. It is a non-linear operation, and the function f(n) = n² is continuous and differentiable over real numbers. The graph of y = n² is a parabola opening upwards, symmetric about the y-axis. The inverse operation of squaring is taking the square root.

The concept of squaring appears across various disciplines, including algebra, physics, and engineering, often relating to calculating areas, energies, and other quadratic quantities. Its simplicity and mathematical properties make it a fundamental concept in both theoretical and applied sciences.