the sum of the rational terms in the binomial expansion of (2^1/2 + 3^1/5)^10 ??

Given binomial expansion is, 212+31510So,Tr+1=Cr1021210-r315r,     Where r=0,1,2,....10For rational term,r=multiple of 5=0,5,10                           ......110-r=multiple of 2=0,2,4,6,8,10         ......2From equation 1 and 2, the possible values of r is 0 and 10.
Thus, sum of rational terms=T0+1+T10+1                                                   =C01021210-03150+C101021210-1031510                                                   =1×25×1+1×1×32                                                   =32+9                                                   =41Hence, sum of rational terms in given binomial expansion  is 41.

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