Question

show that root 2 is an irrational no.
for 3 marks
pls explain every step as I am not able to understand

no irrelevant answer
no spam ​

Answer 1

Given √2 is irrational number.

Let √2 = a / b where a,b are integers b ≠ 0 .

We also suppose that a / b is written in the simplest form .

Now √2 = a / b

⇒ 2 = a² / b²

⇒   2b² = a²

∴ 2b² is divisible by 2

⇒  a² is divisible by 2  

 

⇒  a is divisible by 2  

∴ Let a = 2c

a² = 4c²

⇒ 2b² = 4c²

⇒ b² = 2c²

∴ 2c²  is divisible by 2

∴ b²  is divisible by 2

∴ b  is divisible by 2

∴ a are b are divisible by 2 .

This contradicts our supposition that a/b is written in the simplest form .

Hence our supposition is wrong .

∴ √2 is irrational number.

Answer 2

Answer:

because square root 2 is irrational number