Question

show that ✓2 is irrational
​

Answer 1

Answer:

hope it helps u dear

please thank my all answer

Answer 2

To prove : √2 is irrational.

We will prove whether √2 is irrational by contradiction method.

Let √2 be rational 

It can be expressed as √2 = a/b ( where a, b are integers and co-primes. 

=>√2 = a/b

=>2= a²/b² 

=>2b² = a²

It means 2 divides a²

By the Fundamental theorem of Arithmetic

By the Fundamental theorem of Arithmetic so, 2 divides a .

Let a = 2k (for some integer) 

=>a² = 4k² 

=>2b² = 4k² 

=>b² = 2k² 

2 divides b²

Similarly,

2 divides b. 

Now 2 divides both a & b this contradicts the fact that they are co primes. 

This happened due to faulty assumption that √2 is rational. Hence, √2 is irrational.

Hope it helps you ✔️