Squared — Definition, Formula & Examples

Squared means multiplying a number by itself. For example, 5 squared is 5 × 5, which equals 25.

To square a number $a$ is to raise it to the second power, producing $a^2 = a \times a$ . The result is called a perfect square when $a$ is an integer.

Key Formula

a^2 = a \times a

Where:

$a$ = The base — the number being squared
$2$ = The exponent, indicating the base is multiplied by itself

How It Works

Write the number, then place a small 2 as a superscript to show it is being squared. This tells you to multiply the number by itself exactly once. Squaring always produces a non-negative result when the input is a real number, because a negative times a negative is positive. For instance,

(-3)^2 = (-3) \times (-3) = 9

Worked Example

Problem: Find the value of 8 squared.

Write the expression: Use the exponent notation.

8^2

Multiply the base by itself: Multiply 8 by 8.

8 \times 8 = 64

Answer:

8^2 = 64

Why It Matters

Squaring appears in the Pythagorean theorem, area formulas, and the distance formula — all topics you will encounter repeatedly in geometry and algebra. Understanding it is also essential for working with quadratic equations in high school math.

Common Mistakes

Mistake: Confusing squaring with doubling. Students sometimes calculate

5^2

5 \times 2 = 10

instead of

5 \times 5 = 25

Correction: The exponent 2 tells you how many times the base appears as a factor, not what you multiply by.

5^2

means two factors of 5:

5 \times 5