Question

me pueden explicar como extraer factores fuera del radical usando este ejemplo?

Ej: √ 48x²

Answer 1

Respuesta:

Exact result:

4 sqrt(3) sqrt(x^2)

diferentes metodos:

Alternate form assuming x is real:

4 sqrt(3) abs(x)

Alternate form assuming x>0:

4 sqrt(3) x

Root:

x = 0

Properties as a real function:

Domain

R (all real numbers)

Range

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

Parity

even

Series expansion at x = 0:

(4 sqrt(3) sqrt(x^2) x)/x + O(x^9)

(Puiseux series)

Series expansion at x = ∞:

4 sqrt(3) x + O((1/x)^9)

(Taylor series)

Derivative:

d/dx(sqrt(48 x^2)) = (4 sqrt(3) x)/sqrt(x^2)

Indefinite integral:

integral4 sqrt(3) sqrt(x^2) dx = 2 sqrt(3) x sqrt(x^2) + constant

Global minimum:

min{sqrt(48 x^2)} = 0 at x = 0

Series representations:

sqrt(48 x^2) = sqrt(-1 + 48 x^2) sum_(k=0)^∞ (-1 + 48 x^2)^(-k) binomial(1/2, k) for abs(1 - 48 x^2)>1

sqrt(48 x^2) = sum_(k=0)^∞ ((-1)^k (-1 + 48 x^2)^k (-1/2)_k)/(k!) for abs(1 - 48 x^2)<1

sqrt(48 x^2) = sqrt(-1 + 48 x^2) sum_(k=0)^∞ ((-1)^k (-1 + 48 x^2)^(-k) (-1/2)_k)/(k!) for abs(1 - 48 x^2)>1

espero te sirva