Question

If P is a prime number then show that root P is irrational search days

Answer 1

see you should do this like proving √2 is drrational

let √p be a rational number
so √p=a/b where a and b are coprimes
so p=a2/b2
so
a2 is divisible by p 
=> a is divisible by p 
So, we can write a = pc for some integer c. 
Therefore, a2 = p2c2 ….[Squaring both the sides] 
=> pb2 = p2c2 ….[From (i)] 
=> b2 = pc2 
=> b2 is divisible by p 
=> b is divisible by p 
=> p divides both a and b. 
=> a and b have at least p as a common factor. 
But this contradicts the fact that a and b are coprime. 
This contradiction arises because we have 
assumed that √p is rational. 
Therefore, √p is irrational.

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