A term in the binomial expansion of (a+b)n is given by Tk+1=C(n,k)×an−k×bk. For a term to be rational, the exponents of both √‌3 and 51∕4 must be integers. Formula Used: In (√‌3)n−k,n−k must be even for it to be rational. In (51∕4)k,k must be a multiple of 4 for it to be rational. Calculation: Let n=12 : ⇒ For √‌3n−k to be rational, n−k must be even. ⇒ Since n=12,k must also be even. ⇒ For (51∕4)k to be rational, k must be a multiple of 4 . ⇒ The values of k that satisfy both conditions ( k is even and a multiple of 4 ) are: ⇒k=0,4,8, and 12. ⇒ These correspond to 4 rational terms in the expansion.