I am reading this question: shortest distance from point to hyperplane lagrange method
And in the answer, it directly says "Consider the Lagrangian function" $$L(\mathbf x,\lambda)=\|\mathbf x-\mathbf x_0\|^2+2\lambda(\mathbf w^T\mathbf x+b)$$
My question is: $$\|\mathbf x-\mathbf x_0\|^2$$
Why is this term squared without squared root? and how to understand the whole Lagrangian function? Any help is appreciated.