Question

prove that 5+ root 3 is an irrational number.

Answer 1

RTP:-5-2_/3 IS IRRATIONAL NO.

PROOF:- LET US ASSUME ON OUR CONTRARY 5-2_/3 BE IRRATIONAL

=> 5-2_/3=a/b (since it is rational) and a and b are integers with no common factor

=> (5-a)/b=2_/3

=> (5b-a)/2b=_/3

since we get integer divided by integer this means that _/3 is rational but we know that root 3 irrational so our contrary is wrong

and thus 5-2_/3 is irrational.