Question

Prove this √2 is an
irrational number​

Answer 1

Answer:

Here's the answer to your asked question..

Answer 2

Answer:

This can be soved by the rule of contradiction

Step-by-step explanation:

First assume that √2 is a rational number.

So it can be expressed in the form p/q where p, q are co-prime integers and q≠0

Hence √2 = p/q

On squaring both the sides we get,

=>2 = (p/q)²

=> 2q² = p²……………………………..(1)

p²/2 = q²

So 2 divides p and p is a multiple of 2.

⇒ p = 2m

⇒ p² = 4m² ………………………………..(2)

From equations (1) and (2), we get,

2q² = 4m²

⇒ q² = 2m²

⇒ q² is a multiple of 2

⇒ q is a multiple of 2

Hence, p, q have a common factor 2. This contradicts our assumption that they are co-primes. Therefore, p/q is not a rational number

√2 is an irrational number.