Question

prove that one by root 2 is an irrational number....
NEED EXPLANATION..​

Answer 1

Answer:

This process is true for any rational number, that is, a rational number that is not already in co-prime form can be reduced to co-prime form. ... In this proof we want to show that √2 is irrational so we assume the opposite, that it is rational, which means we can write √2 = a/b.

follow,,,mee

Answer 2

Answer:

√2 = p/q

On squaring both the side 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.