prove that√2 is an irrational number ?
Answers
QuestionsMaths QuestionsProof That Root 2 Is An Irrational Number
Top Banner
Proof that root 2 is an irrational number.
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.
(life bhot kimti h apni life kisi papa ki pari ke liye waste na kro)
Answer:
open ehe attachment
Step-by-step explanation:
hope it helps
