Prove that root5 is irrational

1.	Prove that root5 is irrational
Answer» Let root5 is a rational number where root5=a/b and b is not = 0Thenroot5 =a/bSquaring both side5=a×a/b×b5bsquare=a squarea is divisible by 55 is a factor of aLet 5c=aThen5bsquare =(5c)square5bsquare =25csquarebsquare = 5csquareThenbsquare is a factor of 5b is also a factor of 5Hence,a and b are co prime numbers Therefore,our contradict the fact that root5 is an irrational number Hence,our supposition is wrong Therefore, root5 is an irrational number Hence Proved

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