Question

prove that 5 - 2 root 3 is irrational ​

Answer 1

Step-by-step explanation:

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.