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Prove tha root 2 is irrestional

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Prove tha root 2 is irrestional
  • 1 answers

Sahana Parashetti 1 year, 2 months ago

Let assume √2 is rational then √2 = p/q next square on both side after squaring root and square get cancel remaining is 2 then rhs side p2/q2 then take q2 lhs side it becomes 2q2 then p2 remains in rhs side then take 2 to rhs side it becomes p2/2 then next write 2 divides p2 and p also next take q2=p2/2 as equation 1 let p =2c then it becomes q2=(2c)2/2 then q2 =4c2/2then q2=2c2 then take 2 lhs side it becomes q2/2= c2 then write 2 divides q2and q also next step p and q has 2 as Common factor this contradiction as arise because of our assumption is wrong that root 2 is a rational number therefore root 2 is an irrational number
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