Show that V2 is irrational.

1.	Show that V2 is irrational.
Answer» Let us assume that √2 is rational Thus √2= a / b where a,b are integers b ≠ 0we 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 Thus 2c2 is divisible by 2 Thus b2 is divisible by 2 Thus b is divisible by 2 Thus 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 Hence √2 is irrational number.

Answer»

Let us assume that √2 is rational

Thus √2= a / b where a,b are integers b ≠ 0we 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

Thus 2c2 is divisible by 2

Thus b2 is divisible by 2

Thus b is divisible by 2

Thus 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

Hence √2 is irrational number.

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