Prove that )5 is irrational number

1.	Prove that )5 is irrational number
Answer» Let take √5 as rational numberIf a and b are two co prime number and b is not equal to 0.We can write √5 = a/bMultiply by b both side we getb√5 = aTo remove root, Squaring on both sides, we get5b² = a² ……………(1)Therefore, 5 divides a² and according to theorem of rational number, for any prime number p which is divides a² then it will divide a also.That means 5 will divide a. So we can writea = 5cand plug the value of a in equation (1) we get5b² = (5c)²5b² = 25c²Divide by 25 we getb²/5 = c²again using same theorem we get that b will divide by 5and we have already get that a is divide by 5but a and b are co prime number. so it is contradicting .Hence √5 is a non rational number Kindly check here for answer

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