Question

______________ is the irrational number.
1) √2
2)√4
3) 3
4) 0
please answer fast​

Answer 1

Answer:

$\sqrt{2}$

it is the irrational number

Answer 2

Answer:

√2

Step-by-step explanation:

Let us 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

√2 = p/q

Here p and q are coprime numbers and q ≠ 0

Solving

√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.

here, √4 is 2. so it's not irrational

3 and 0 are whole numbers and they are not irrational as they can be represented as 3/1 and 0/1, but 0/1 is 0 itself, so it is just an whole number