Question

How to show that root 2 irrational

Answer 1

when we divide 2 with the help of long division we can see that its value is 1.414...... this number shows that it is a never ending number which means that it is an irrational number

Answer 2

Answer:

Step-by-step explanation=

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.