A root equation is an equation in which a root form is present. A common scheme for solving such an equation is as follows:

1. Isolate the root form.
   
   
2. Take the squares of the left- and right-hand sides and solve the resulting equation.
   
   
   
   
   
3. Check whether the solutions of the squared equation are valid solutions of the original equation

Example

1. isolate the root: $\sqrt{x+3}=x+1$
   
   
2. Square and solve:
   $x+3=(x+1)^2=x^2+2x+1$ gives $x^2+x-2=0$ or $(x+2)(x-1)=0$ and so
   $x=-2$ or $x=1$.
   
   
3. Substitution of $x=-2$ into $\sqrt{x+3}=x+1$ gives $1=-1$ and therefore $x=-2$ is not a valid solution.
   The solution $x=1$ is valid.