Solve \sqrt{x}=x^2

Evaluate

x = x^{2}

Find the domain

x = x^{2}, x \geq 0

Raise both sides of the equation to the 2 -th power to eliminate the isolated 2 -th root

(x)^{2} = (x^{2})^{2}

Evaluate the power

x = x^{4}

Move the expression to the left side

x - x^{4} = 0

Factor the expression

x (1 - x^{3}) = 0

Separate the equation into 2 possible cases

x = 0 1 - x^{3} = 0

Solve the equation

More Steps

x = 0 x = 1

Check if the solution is in the defined range

x = 0 x = 1, x \geq 0

Find the intersection of the solution and the defined range

x = 0 x = 1

Check the solution

More Steps

x = 0 x = 1

Check the solution

More Steps

x = 0 x = 1

Solution

x_{1} = 0, x_{2} = 1

Solve the equation