prove that √3 is irrational
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Answer:
√3 is irrational because it is non repeating and non reoccurring number.
it's value is √3=1.73205081........
Let us start with the contrary, √3 is a rational number.
Hence √3 = a/b ..................(1)
where a and b are prime integers and no comman factor between a and b.
hence √3b = a
By squaring both sides, 3b2 = a2 or a2 / 3 = b2 ..............(2)
eqn.(2) shows 3 is a factor of a2 . If a is a prime number, then 3 also should be factor of a.
If 3 is a factor of a, then this contradicts the assumption we made for eqn.(1), that a is a prime number.
Hence √3 is not a rational number , it is an irrational number.
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