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Anybody ans me fast.....

prove that \/''''' 3 ( root 3 ) is an irrational number.......
what do u want to prove, is it 33333333333333333333...*root 3


Let v!3 be rational number                (NOTE ! is denoted for root)
v!3=a%b                                                sq=square of the variable in bracket

squarring on both sides
a&(a)sq factors  vq                     (let (a)sq =c)
c&(c)sq also factors vq
it contradicts our statement it has two factors
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Let us assume to the contrary that √3 is a rational number.
Therefore √3 = p/q ,where p & q are co-prime & q≠0
So,         (√3)²= p²/q²
⇒              3   = p²/q²
⇒            3*q²= p²
So p² is divisible by 3,so p is also divisible by 3
⇒p² is divisible by 9.
                3    = p²/q²
⇒             q²   = p²/3
So,q² is also divisible by 3.
So p & q are not co-prime.
Therefore √3 is an  irrational number.

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