Find expected value of root of a sample variance

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It is easy to compute $E(s^2)=E(\frac{1}{n-1}\sum_{i=1}^{n}(x_i-\bar{x})^2)=\sigma^2$. My question is - how can E(s) be calculated?

I'm trying to use $\frac{s^2(n-1)}{\sigma^2}$ has Chi-square distribution, but it does not help a lot.