Question

prove that √13 is irrational

Answer 1

Let us assume that √13 is rational no and equals to p/q are Co primes
√13=p/q
squaring both sides
√13*2=p*2/q*2
13=p*2/q*2
13q*2=p*2
13/p*2
13/p
p=3r for some integer r
p*2=169r*2
13q*2=169*2
b*2=13r*2
13/b*2
13/b
13 is a common factor but this is contradiction hence our supposition is wrong √13 is irrational no

Answer 2

Take a look at this pic