Prove 2+root 3 /5 is a irrational no. , given that root 3 is a irratio

1.	Prove 2+root 3 /5 is a irrational no. , given that root 3 is a irrational no.
Answer» Let take 2√ 3/5 is rational no.Then we can write that 2√3/5=r/s where r and s are integers and s not equal to 0. Then r and s has common factor other than 1.=>2√3/5 = a/b=> 2√3=5a/b=>√3=5a/b*1/2=>√3=5a/2b(here 5a and 2b are integers as a and b are the common factor other than 1 so 5a and 2b are also integers)But this contradicts the fact that √3 is irrational .This problem arisen because of our assumption so our assumption is wrong .Hence,we conclude that 2√3/5 is irrational no.

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