Squared

The term 'squared' describes the result of multiplying a number by itself. It's a fundamental mathematical operation used extensively in algebra, geometry, and various scientific fields. When a number is squared, the result is always non-negative because a negative multiplied by a negative results in a positive. The operation can be represented using an exponent of 2 (x²), where 'x' represents the number being squared. Beyond numerical context, 'squared' can also describe something that is in a rectangular shape with equal sides and right angles or being brought to conformity.

Squared meaning with examples

• In the equation x² = 9, the solution is x = 3 and x = -3, since both 3 squared and -3 squared equal 9. Understanding this is crucial for solving quadratic equations and working with exponents. This demonstrates the inverse operation of finding the square root.
• The area of a square with sides of length 5 units is calculated by squaring the side length: 5² = 25 square units. Geometry heavily relies on this concept for calculating areas, volumes, and other geometric properties. This underscores the relationship between multiplication and geometric forms.
• To analyze the variance in a dataset, each deviation from the mean is squared to eliminate negative values and give each data point equal impact. Statistical analysis leverages squaring to address the magnitude of deviations and quantify data spread. This method ensures that outliers are considered more significantly.
• The engineer needed to find the squared value of the voltage, and that value was 144 to be used in an equation for resistance. Physics and engineering often use squared values such as velocity and acceleration to represent energy and rates of change. This operation can reveal hidden relationships in physical phenomena.
• The city planners, as they began to draw up the plans for the city layout, wanted a grid of evenly spaced buildings, resulting in a 'squared' design for the central district. The term takes on a geometric context when used in art, architecture, or urban planning. This demonstrates the use of squared in an alternative context.