how✓2is irrational?

1.	how✓2is irrational?
Answer» 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∴ 2b2is divisible by 2 ⇒ a2is divisible by 2 ⇒ a is divisible by 2 ∴ let a = 2ca2= 4c2⇒ 2b2= 4c2 ⇒b2= 2c2 ∴ 2c2 is divisible by 2 ∴ b2 is divisible by 2 ∴ b is divisible by 2 ∴ a and b are divisible by 2 This contradicts our supposition that a/b is written in the simplest formHence our supposition is wrong ∴ √2 is irrational number.

Answer»

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∴ 2b2is divisible by 2

⇒ a2is divisible by 2

⇒ a is divisible by 2

∴ let a = 2ca2= 4c2⇒ 2b2= 4c2

⇒b2= 2c2

∴ 2c2 is divisible by 2

∴ b2 is divisible by 2

∴ b is divisible by 2

∴ a and b are divisible by 2

This contradicts our supposition that a/b is written in the simplest formHence our supposition is wrong

∴ √2 is irrational number.

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