What is x times x?

x * x, often written as x², represents the square of a number, variable, or expression. Here's some information about it:

• Definition: The expression x * x or x² means multiplying the value of x by itself. This is a fundamental mathematical operation.

• Geometric Interpretation: Geometrically, x² represents the area of a square where each side has length x.

• Algebraic Significance: In algebra, x² is a quadratic term. Quadratic terms appear in quadratic equations and functions, which have a characteristic U-shaped graph called a parabola.

• Calculus: The derivative of x² with respect to x is 2x. The integral of x² with respect to x is (x³/3) + C, where C is the constant of integration.

• Examples:

  • If x = 3, then x² = 3 * 3 = 9.
  • If x = -2, then x² = (-2) * (-2) = 4. (Note that squaring any real number always results in a non-negative value).

• Applications: Squaring a number is used extensively in various fields such as physics (e.g., calculating energy), engineering (e.g., calculating area and volume), and statistics (e.g., calculating variance and standard deviation). Calculating euclidean distance also contains squaring operations.