The total number of irrational terms in the binomial expansion of (7^1/5-3^1/10)^60 is:

Question

The total number of irrational terms in the binomial expansion of $\left(7^{1/5}-3^{1/10}\right)^{60}$ is:

Accepted Answer

$$T_{r+1}=\binom{60}{r}7^{(60-r)/5}(-1)^r3^{r/10}$$

Rational when $r$ is a multiple of $\text{lcm}(5,10)=10$: $r=0,10,20,\dots,60$ --- 7 values.

Total terms $=61$; irrational terms $=61-7=54$

Solutions · 1