Prove that v3 is irrational.

1.	Prove that v3 is irrational.
Answer» Given √3 is irrational number. Let √3 = a / b wher a,b are integers b ≠ 0we also suppose that a / b is written in the simplest form Now √3 = a / b ⇒ 3 = a²/ b² ⇒ 3b²= a² ∴ 3b²is divisible by 3 ⇒ a²is divisible by 3 ⇒ a is divisible by 3 ∴ let a = 3c a²= 3c² ⇒ 3b²= 9c² ⇒b²= 3c² ∴ 3c² is divisible by 3 ∴ b² is divisible by 3 ∴ b is divisible by 3 ∴a are b are divisible by 3this contradicts our supposition that a/b is written in the simplest formHence our supposition is wrong ∴ √3 is irrational number.

Answer»

Given √3 is irrational number.

Let √3 = a / b wher a,b are integers b ≠ 0we also suppose that a / b is written in the simplest form

Now √3 = a / b

⇒ 3 = a²/ b²

⇒ 3b²= a²

∴ 3b²is divisible by 3

⇒ a²is divisible by 3

⇒ a is divisible by 3

∴ let a = 3c

a²= 3c²

⇒ 3b²= 9c²

⇒b²= 3c²

∴ 3c² is divisible by 3

∴ b² is divisible by 3

∴ b is divisible by 3

∴a are b are divisible by 3this contradicts our supposition that a/b is written in the simplest formHence our supposition is wrong

∴ √3 is irrational number.

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