Square root (√x)
Calculate the square root of a number. With graph and explanation.
Graf funkce
Co je square root
The square root √x is the inverse of squaring – it finds the number which, when squared, gives x. For example √9 = 3, because 3² = 9.
Where it is used in practice
- Finding the side of a square from its area.
- Pythagorean theorem – length of the hypotenuse or a leg.
- Statistics: standard deviation is the square root of variance.
Good to know
The square root of a negative number is not defined in the real numbers. √0 = 0. The symbol √ denotes the positive root.
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.