Question

prove 2-3√5 as irrational​

Answer 1

Proof

=> Let us assume, to the contrary, That ( 2 - 3√5 ) is rational

=> Then there exist co - prime a and b ( b ≠ 0 ) Such that

=> 2 - 3√5 = a/b

=> -3√5 = a/b - 2 => (a - 2b)/b

=> √5 = - (a - 2b)/3b

=> Since a and b are integers, So (a - 2b)/3b is rational

=> This √5 is also rational

=> But , This contradicts the fact that √5 is irrational. so , Our assumption is incorrect

Hence 2-3√5 is irrational

More Information

=> Natural number => Counting number 1 , 2 , 3 , 4 ,...... etc are know as natural Number

=> Integers => All Counting Number , negative of counting and 0 form the collection of all integers