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

\[x=\sqrt{x+3}-1\]

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.