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√3 is a irrational number |
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Answer» Lets assume that root3 is rational and it is an positive integer and is equal to a/b .So b is not equal to 0. AND "a" and "b" are co primes. Root3=a/bSquaring on both sides. 3=a square/b square.Sob square = a square /3 ( we can see that a is divisible by 3) .Let a square be c3So b square 3 = c square 9C square = b square/3 ( we can see that b is divisible by 3).As we assumed that a and b are co primes we can conclude that by Fundamental Theorem of Arthematic. Our assumption is wrong .Therefore root 3 is irrational See in chapter 1 on p. g no. 13 |
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