Upper bound for $( a_1 + a_2 + \cdots + a_n)^{1/2}$

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Is there any upper bound for an expression like:

$$\left( a_1 + a_2 + \cdots + a_n\right)^{1/2} ?$$

I need it for $n=3$. I know Hardy's inequality but it is for exponent greater than 1. Is there anything for the square root?