$\sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1} + \frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}$

$\sqrt{\frac{\hat{p}_1}{n_1} + \frac{\hat{p}_2}{n_2}}$

$\frac{\hat{p}_1 - \hat{p}_2}{\sqrt{n_1+n_2}}$

$\sqrt{\hat{p}_1(1-\hat{p}_1) + \hat{p}_2(1-\hat{p}_2)}$