Clarification about inequality in summation

Question

In my work I am facing the following situation, wherein I am trying to compute CDF of random variable $Y$ such that

$F_Y(y) = \text{Pr}(\sum_{m = 1}^M |Z_m|^2\leq \frac{y}{A})$ -----(1)

where $Z$ is a random variable, $y$ is dummy variable, $A$ is a constant and $m$ is index of summation.

My query is can we write eq. (1) as shown below in eq. (2)

$F_Y(y) = \text{Pr}(\sum_{m = 1}^M |Z_m|\leq \sqrt{\frac{y}{A}})$ -----(2)

Any help in this regard will be highly appreciated.