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Articles: Science | Irrational Number - Nazeer
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Irrational Number - Sqrt 3
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Suppose sqrt3 is rational.
Sqrt3 = p/q
[p,q int, q#0, (p,q)=1 ].
(p,q) mean gcd of p&q
Cubing on both sides. {# mean not = }
3 = p'''/q''' [p''' = p cube ]
p''' = 3q'''
q''' divides p'''
q divides p'''
q divides p''
q divides p
[a divides bc and (a,b)=1 then a divides c ]
(p,q)#1
Contradiction.
Sqrt3 is irrational
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