Question

find √2 is an irrational number?

Answer 1

It's totally same just replace 5 with 2.

Hope it is helpful to you

Answer 2

Heya!

Here is yr answer......


Let us assume √2 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

by sub. a=2c in eq. a² = 2b²


(2c)² = (2b)²

4c² = 2b²

2c² = b²

b² = 2c²


Since, 2 divides b²

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


From 1 & 2,

we conclude that a, b are not co-primes.

So, our assumption is false.

Therefore, √2 is irrational!


Hope it hlpz...