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Plot

Root

x = 0

Properties as a real function

{x element R : x>=0} (all non-negative real numbers)

{y element R : y>=0} (all non-negative real numbers)

injective (one-to-one)

Derivative

d/dx(sqrt(x)) = 1/(2 sqrt(x))

Indefinite integral

integral sqrt(x)dx = (2 x^(3/2))/3 + constant

Global minimum

min{sqrt(x)} = 0 at x = 0

Series representation

sqrt(x) = sqrt(-1 + x) sum_(k=0)^∞ (-1 + x)^(-k) binomial(1/2, k) for abs(-1 + x)>1

sqrt(x) = sum_(k=0)^∞ ((-1)^k (-1 + x)^k (-1/2)_k)/(k!) for abs(-1 + x)<1

sqrt(x) = sqrt(-1 + x) sum_(k=0)^∞ ((-1)^k (-1 + x)^(-k) (-1/2)_k)/(k!) for abs(-1 + x)>1