Question

prove that ✓2 is irrational​

Answer 1

Step-by-step explanation:

Given √2 is irrational number.

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

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 so b is divisible by 2

As 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.

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Answer 2

Answer:

root 2 is an irrational number because it is a non perfect square and a prime number.

also root 2= 1.414......which is

• non termaneting
• non recurring

HENCE, IT IS AN IRRATIONAL NUMBER.