√5 prove it is irrational

1.	√5 prove it is irrational
Answer» Let take √5 as a 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 a theorem of rational number, for any prime number p which is divided \'a2\' then it will divide \'a\' also.That means 5 will divide \'a\'. So we can writea = 5cand putting the value of a in equation (1) we get5b2 = (5c)25b2 = 25c2Divide by 25 we getb2/5 = c2again using the same theorem we get that b will divide by 5and we have already get that a is divided by 5but a and b are co-prime number. so it is contradicting.Hence √5 is an irrational number

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