Square (x²)
Calculate the square of a number. With graph, explanation and real-world examples.
Graf funkce
Co je square
Squaring a number means multiplying it by itself: x² = x · x. It is read “x squared”. The result is called a square because it gives the area of a square with side x.
Where it is used in practice
- Area of a square or circle – area grows with the square of the dimension (twice the side = four times the area).
- Pythagorean theorem: c² = a² + b² for finding a side of a right triangle.
- Physics: kinetic energy grows with the square of speed, so double the speed = four times the impact energy.
Good to know
A square is never negative: (−3)² = 9 just like 3² = 9. That is why the square root of a positive number has two solutions (+ and −).
Rules of exponents
When working with powers it helps to know the basic rules, which always hold:
xⁿ · xᵖ = xⁿ⁺ᵖ (product – add the exponents)
xⁿ ÷ xᵖ = xⁿ⁻ᵖ (quotient – subtract the exponents)
(xⁿ)ᵖ = xⁿ·ᵖ (power of a power – multiply)
x⁻ⁿ = 1 / xⁿ (negative exponent)
x^(1/n) = ⁿ√x (root as a power)
In detail with examples: rules of exponents.
Tip: very large numbers are shown in shortened form – use scientific notation.