examine whether √2 is rational or irrational with full process​

2 thoughts on “examine whether √2 is rational or irrational with full process​”

1. Answer:

   given √2

   To prove: √2 is an irrational number.

   Proof:

   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.

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2. Step-by-step explanation:

   [tex]\huge\fbox\orange{❥︎Answer}[/tex]

   ➢ √2 is an irrational number.

   Refer to the attachment.

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