Question

if P is a prime number then prove that root p is irrational

Answer 1

HOLA !!

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Refer the attachment

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HOPE U UNDERSTAND ☺☺

Answer 2

Hey! ! !

Solution :-

☆ Let us assume, to the contrary, that √p is 
rational. 
So, we can find coprime integers a and b(b ≠ 0) 
such that √p = a/b 
=> √p b = a 
=> pb2 = a2 ….(i) [Squaring both the sides] 
=> 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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☆ Regards :- ♡♡《 Nitish kr singh 》♡♡