Question

prove that under root 11 is irrational number

Answer 1

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If possible, Let root 11 be a rational number and Let its Simplest form be A/B


Where,


A and B are some integer having no common factor other than 1
Now,



root 11 = A/B


On squaring both sides we get,




11 = A² /B²



=> 11B² = A² ---------(1)




=> 11 divides A²



=> 11 divides A



Let A = 11C for some integer C




Putting A = 11C in (1) , we get



11B² = 121C²




=> B² = 121C² /11




=> B² = 11C²




=> 11 Divides B²





=> 11 Divides B



Thus,



11 is a common factor of A and B.



But,


This contradicts the fact that A and B have no common factor other than 1.


This Contradiction arises by assuming that root 11 is rational number.





Hence,



root 11 is irrational number .




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