Question

prove that the following number is an irrational *
root 11

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Answer 1

Step-by-step explanation:

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Just replace 'n' by 11

Answer 2

Step-by-step explanation:

Let us assume on the contrary that√2 is a rational number. then, there exist positive integers a and b such that

√2=a/b where,a and b, are co-prime i.e. their

HCF is 1

= (√2)²=(a/b)²

=2=a²/b²

=2b²=a²

=2 | a² [.'. 2 | 2b² and 2b²= a²]

=2 | a =(i)

= a= 2c for some integer c

= a²=4c²

= 2b²=4c² [.'. 2b² = a²]

= b²=2c²

=2 | b² [.'. 2 | 2c²]

= 2 | b … (ii)

from (i) and (ii), we obtain that 2 is a common factor of a and b, but, this contradicts the fact that a and b have no commom factor other than 1. This means that our supposition is wrong

Hence,√2 is an irrational number.