# Solved – Why does \$l_2\$ norm regularization not have a square root

Specifically talking about Ridge Regression's cost function since Ridge Regression is based off of the $$l_2$$ norm. We should expect the cost function to be:

$$J(theta)=MSE(theta) + alphasqrt{sum_{i=1}^{n}theta_i^2}$$

Actual:

$$J(theta)=MSE(theta) + alphafrac{1}{2}sum_{i=1}^{n}theta_i^2$$

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Also, minimizing $$MSE$$ subject to $$|theta|_2le c$$ is equivalent to minimizing $$MSE$$ subject to $$|theta|_2^2le c^2$$.