$(|x_1|+|x_2|+...+|x_n|)$ vs $\sqrt{(|x_1|^2+|x_2|^2+...+|x_n|^2)}$, which is larger and why?

Question

Actually, I know which is larger. Is there some kind of rule that states that the square root is less or equal to the first expression?

** My tag is probably incorrect **

Ahmed's answer below uses essentially the same idea, so feel free to accept his answer. — Wojowu, Nov 26 '15 at 15:54

score 8 · Accepted Answer · answered Nov 26 '15 at 15:51

8

$$(\sum_{i=1}^n |x_i|)^2 = \sum_{i=1}^n |x_i|^2 + 2\sum_{1 \le i < j \le n} |x_i| |x_j| \ge \sum_{i=1}^n |x_i|^2 $$

answered Nov 26 '15 at 15:51

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