A simple inequality and root I need to use the following inequality
$$ \left(\sum_{i=1}^N X_i \right)^{1/2} \leq \left( \sum_{i=1}^N X_i^{1/2} \right),\hspace{0.5cm} 0 \leq X_i $$
But i can't remember its name.
Is the inequality correct?
If it's correct, then how can i prove it?

$$\sum_{i=1}^nX_i^{\frac{1}{2}}=\sqrt{\left(\sum_{i=1}^nX_i^{\frac{1}{2}}\right)^2}=\sqrt{\sum_{i=1}^nX_i+2\sum_{1\leq i<j\leq n}^nX_i^{\frac{1}{2}}X_j^{\frac{1}{2}}}\geq\sqrt{\sum_{i=1}^nX_i}$$
