# Proof of square root properties

1. Sep 4, 2011

### diracy

1. The problem statement, all variables and given/known data
$\sqrt{\sum}x^{2}_{i}$$\leq$$\sum$|x$_{i}$|$\leq$$\sqrt{n}$$\sqrt{\sum}x^{2}_{i}$

*The sums are all from i=1 to n.*

2. Relevant equations

3. The attempt at a solution
I'm very new to proof-based math, and just looking for some help to get started with this one. Thanks in advance.

2. Sep 4, 2011

### lanedance

For this part
$$\sqrt{\Sum_i x_i^2} \leq \Sum_i |x_i|$$

it should be clear
$$0 \leq \sqrt{\Sum_i x_i^2}$$
$$0 \leq \leq \Sum_i |x_i|$$

so squaring both sides could be useful

3. Sep 6, 2011

### diracy

I tried that and didn't get far. It seems to my the leftmost inequality is always equal. I must be thinking about it wrong. In what instance would that inequality be less than?

4. Sep 7, 2011

### lanedance

you should some cross terms like |xi||xj| on in the middle, which don't appear on the left