Question

prove that root 7 is not rational number​

Answer 1

Answer:

√7 = p/q

On squaring both the side we get,  

=> 7 = (p/q)2  

=> 7q2 = p2……………………………..(1)  

=>p2/7 = q2

So 7 divides p and p and p and q are multiple of 7.

⇒ p = 7m  

⇒ p² = 49m² ………………………………..(2)

From equations (1) and (2), we get,

7q² = 49m²  

⇒ q² = 7m²

⇒ q² is a multiple of 7  

⇒ q is a multiple of 7  

Hence, p,q have a common factor 7. This contradicts our assumption that they are co-primes. Therefore, p/q is not a rational number

√7 is an irrational number.

Step-by-step explanation: