We note that given a probability distribution function $P$ over a space $U$ the expected value of a function of the elements in U:
$$ E(f(x)) = \int_{U} f(x)P(x) $$
We thus consider the mean as the expected value of the numbers that is:
$$ E(x) = \int_{U} x P(x) $$
Now we consider "standard deviation" to be the expected difference between a variable from the mean that is
$$ Std(x) = E(|x - E(x)|) = E\left(\sqrt{(x - E(x))^2}\right) $$
Yet Standard deviation is always measured as:
$$ \sqrt{E((x - E(x)^2)} $$
The latter formula doesn't make sense to me. Can someone explain why mine is wrong and hte latter is corret?