Question

Prove that root5 is irrational in contradiction method

Answer 1

Answer:

Let root 5 is rational number

a÷b =√5 , a & b are co-prime

a = b√5

squaring both sides

a^2 = (b√5)^2

a^2 = 5b^2. ----------- (1)

a^2 is divides by 5 than a is also divides by 5

Again , take

a = 5c

a^ 2 = (5c)^2

a^2 = 25c^2. ------------(2)

from 1 & 2 ,we get

5b^2 = 25c^2

b^2 = 5c^2

b^2 is divides by 5 than b is also divides by 5

than 5 is common factor of a & b

it is contradiction, because a & b are co- prime

so, √5 is a irrational number