Question

prove that under root 2 is irrational ​

Answer 1

Answer:

specificallythe grief discovered that the diagonals of a square whose sides are 1 unit long has a diagonal length cannot be reached by the peter guardian The oram the length of the diagonal = square root of 2 so the square root of 2 is irrational

Answer 2

Answer:

Given √2

To prove: √2 is an irrational number.

Proof:

Letus assume that √2 is a rational number.

So it t 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.

Step-by-step explanation:

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