Atoms: JEE Mains 2022 June 29 Shift 1

$\sqrt{d_1}$ and $\sqrt{d_2}$ are the impact parameters corresponding to scattering angles $60^\circ$ and $90^\circ$ respectively, when an $\alpha$ particle is approaching a gold nucleus. For $d_1=x\,d_2$, the value of $x$ will be ______.