√(d_1) and √(d_2) are the impact parameters corresponding to scattering angles 60^° and 90^° respectively, when an α particle is approaching a gold…

$\displaystyle \sqrt{\mathrm{d}_1}$ and $\displaystyle \sqrt{\mathrm{d}_2}$ are the impact parameters corresponding to scattering angles $\displaystyle 60^{\circ}$ and $\displaystyle 90^{\circ}$ respectively, when an $\displaystyle \alpha$ particle is approaching a gold nucleus. For $\displaystyle \mathrm{d}_1=x \mathrm{~d}_2$, the value of $\displaystyle x$ will be \_\_\_\_.