$\sqrt{d_1}$ 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 $\mathrm{d}_1=\mathrm{x} \mathrm{d}_2$, the value of x will be $\_\_\_\_$ .
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