Question

1. Show that V2 is not a rational number.​

Answer 1

Step-by-step explanation:

Let us assume that √2 is a rational number and a and b are Co - prime number..

• √2 = a/b
• √2b = a
• squaring on both sides
• = (√2b)² = a²
• = 2b² = a² ......... (i)
• = b² = a² / 2

a² is divisible by 2 it means a is also divisible by 2.

Now, for some integer a = 2c

• put the value of a in 1 equation
• 2b² = (2c)²
• 2b² = 4c²
• b² = 4c²/ 2
• b² = 2c²
• c² = b²/2

b² is divisible by 2 it means b is also divisible by 2.

But it contradicts the fact that a and b are Co prime number.

This contradiction has arisen because of our incorrect assumption that is √2 is rational. So we conclude that √2 is irrational number..