Question

show that root 2 is irrational

Answer 1

Heya!

Here is yr answer.....


Let us assume √2 is rational!

=> √2 = a/b (a, b are co-primes)

=> b√2 = a

by squaring on both sides.....

=> 2b² = a²

=> a² = 2b²

Here, 2 divides a²

Therefore, 2 also divides a ------(1)


Let a = 2c

=> (2c)² = 2b²

=> 4c² = 2b²

=> 2c² = b²

=> b² = 2c²

Here, 2 divides b²

Therefore, 2 also divides b ----(2)



From (1) & (2)

We can conclude that, a , b are nkt co-primes!

Hence, our assumption is false

Therefore, √2 is irrational!

HENCE PROVED!!


Hope it hlpz..

Answer 2

I think it is helpful...