Calculate the square of any number with step-by-step solutions, perfect square detection, and geometry connections.
Square
49
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72 = 49
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Given number: 7
Formula: n^2 = n x n
Calculation: 7^2 = 7 x 7
Result: 49
Square
49
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).
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.
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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
Square
49