显然加减乘法封闭,只需验证除法封闭
(a+b√3)/(c+d√3)
=(a+b√3)(c-d√3)/[(c+d√3)(c-d√3)]
=[(ac-3bd)+(bc-ad)√3]/(c^2-3d^2)
=(ac-3bd)/(c^2-3d^2)+[(bc-ad)/(c^2-3d^2)]√3∈Q(√3)
故Q(√3)是数域