For every $p>0$, there exist constants $A_p>0$ and $B_p>0$ such that for every $n\in\mathbb N$, every $a_1,\ldots,a_n\in\mathbb R$, and independent Rademacher random variables $\varepsilon_1,\ldots,\varepsilon_n$, \begin{align*} A_p\left(\sum_{i=1}^n a_i^2\right)^{1/2} \le \left(\mathbb E\left[\left|\sum_{i=1}^n a_i\varepsilon_i\right|^p\right]\right)^{1/p} \le B_p\left(\sum_{i=1}^n a_i^2\right)^{1/2}. \end{align*}