Question

prove under root of 2 is irrational number

Answer 1

Hii friend,

To prove : ✓2 is irrational Number

Proof :- If possible , let ✓2 be rational Number and let it's simplest form be a/b .

Then , a and b are integers having no Common factor other than 1.

Now,

✓2 = a/b

2 = a²/b². [ On squaring both sides]

2b² = a².........(1)

2 divides a²

Therefore,

2 divides a

Let a = 2C.

Putting a= 2C ,in equation (1)

2b² = a²

2b² = (2C)²

2b² = 4C²

b² =4C²/2

b² = 2C²

2 Divides b² => 2 Divides b .


Thus,

2 is a common factor of a and b.

But , this contradicts the fact that a and b have no Common factor other than 1.

This contradiction arises by assuming that ✓2 is rational.

Hence,

✓2 is irrational Number..... PROVED........




HOPE IT WILL HELP YOU...... :-)