Question

find the term which does not contain irrational expression in the expansion of(5√3+7√2)^24.

Answer 1

Answer:

13 ( Total number of rational terms)

Step-by-step explanation:

General term Tr in the expansion (5√3+7√2)²⁴ is given by

24Cr(5√3)^r(7√2)^24-r where r ranges from 0 to 24.

Now, for the term not to contain any irrational expression, it should be free of radicals, i.e., r should be even as well as 24-r should be even.

Whenever r is even , 24-r is even even henc all the terms where r is even doe not contain any irrational terms.

In total there are 13 rational term starting from r =0,2,4...24.