Simplify. 13 squared=
The Correct Answer and Explanation is:
The expression ( 13 \, \text{squared} ) means ( 13 \times 13 ). When we multiply 13 by itself, we get:
[
13 \times 13 = 169
]
So, ( 13 \, \text{squared} = 169 ).
Explanation of Squaring and its Applications
When a number is squared, it means the number is multiplied by itself. In mathematical terms, squaring a number ( x ) is represented as ( x^2 ). This notation, ( x^2 ), is called an exponent, where 2 is the exponent or “power,” indicating that the base number ( x ) should be multiplied by itself once (in this case, ( x \times x )).
The concept of squaring numbers is common in various fields of math and science. For example, in geometry, the area of a square with sides of length 13 is calculated as ( \text{side} \times \text{side} = 13 \times 13 = 169 ). This is why the operation is called “squaring”—it represents the area of a square.
Squaring as an Operation in Math
Squaring helps simplify expressions, solve equations, and understand properties of numbers. Positive numbers squared will always result in a positive value, as the product of two positive numbers is positive, and similarly, a negative number squared also results in a positive value because the product of two negative numbers is positive (e.g., ( (-13) \times (-13) = 169 )).
Practical Applications
In physics, squaring is used in formulas to calculate energy, area, and other concepts. For instance, kinetic energy is calculated using the square of velocity in the formula ( \text{KE} = \frac{1}{2}mv^2 ), where ( v ) represents velocity. Here, squaring the velocity emphasizes how a small increase in speed significantly increases kinetic energy.
In summary, squaring numbers like 13 helps in calculations and is foundational in math and science, with applications that range from simple geometry to advanced physics.