Question

show that 2 - 3 root 5 is irrational number

Answer 1

let us assume that 2-3√5 is rational.
so 2-3√5 = a/b (b ≠ 0)
now a/b will be reduced to a form where both a and b are co-primes (having no common factors other than one)
⇒ 3√5 = 2- a/b
⇒ √5 = (2- a/b) / 3
here, a, b, 2 and 3 all are integers so (2- a/b) / 3 is rational.
but this contradicts the fact that √5 is irrational (as we know it is irrational)
this contradiction has rise due to our wrong assumption of 2-3√5 is rational.
 hence, it is irrational.
 
           

Answer 2

answer is in pic..............................