Question

Explain by contradiction method that root 2 is an irrational number

Answer 1

Answer: To prove √2 is irrational

So first we assume that √2 is rational

So we can write √2 in the form of a/b

where a and b are co primes

√2=a/b

square both sides

2=a2/b2                                

                      cross multiply

2b2= a2     --  eq1

from a theorem ,  we proved that 2 divides a2

so 2 divides a , hence 2 is a factor of a

instead of b , take c another integer

2c = a        because 2 divide

square both sides

4c2 =  a2  

replace with eq1

4c2= 2b2

simplify

2c2= b2

similarly we can prove by the theorem that 2 divides b2, that means 2 is a factor of b

But this is not possible and its given that a and b are co primes and they only have one factor

hence √2 is irrational

Step-by-step explanation: