Square Calculator
Calculate the square of any number with step-by-step solutions, perfect square detection, and geometry connections.
n^2 = n x nResult
Square
49
Enter a Number
Enter any number (positive, negative, or decimal)
72 = 49
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Step-by-Step Solution
Given number: 7
Formula: n^2 = n x n
Calculation: 7^2 = 7 x 7
Result: 49
Result
Square
49
?How Do You Square a Number?
To square a number, multiply it by itself: n^2 = n x n. For example, 5^2 = 5 x 5 = 25. Perfect squares are numbers like 1, 4, 9, 16, 25 that result from squaring whole numbers. Negative numbers squared become positive: (-3)^2 = 9. Squaring is used in geometry to calculate area of squares (side^2) and in the Pythagorean theorem (a^2 + b^2 = c^2).
What is Squaring?
Squaring a number means multiplying that number by itself. The notation n^2 (read as 'n squared') represents n times n. This operation is fundamental in mathematics, appearing in geometry (area calculations), algebra (quadratic equations), physics (kinetic energy), and statistics (variance). Perfect squares are integers that result from squaring whole numbers.
Key Facts About Squares
- Squaring means multiplying a number by itself: n^2 = n x n
- Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100...
- Negative numbers squared are always positive: (-5)^2 = 25
- Zero squared equals zero: 0^2 = 0
- Area of a square = side length squared
- Squaring is the inverse of taking the square root
- The Pythagorean theorem uses squares: a^2 + b^2 = c^2
- Square numbers always end in 0, 1, 4, 5, 6, or 9
Practice Squaring Numbers
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Practice with 5 problems to test your understanding.
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Frequently Asked Questions
Squaring a number means multiplying it by itself. For example, 5 squared (5^2) equals 5 x 5 = 25. The result is called a "perfect square" when the input is an integer.
The square of a negative number is always positive because a negative times a negative equals a positive. For example, (-4)^2 = (-4) x (-4) = 16. However, be careful with notation: -4^2 = -(4^2) = -16, which is different from (-4)^2 = 16.
A perfect square is an integer that results from squaring another integer. Examples include 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, etc. These are the squares of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, respectively.
The square of a number n represents the area of a square with side length n. For example, a square with sides of 5 units has an area of 5^2 = 25 square units. This is why we call it "squaring" a number.
(-n)^2 squares the entire negative number, giving a positive result. -n^2 only squares n, then applies the negative sign, giving a negative result. For example: (-3)^2 = 9, but -3^2 = -9. The parentheses make a crucial difference!
Last updated: 2025-01-15
Result
Square
49