Question

how to represent root 6 as irrational ​

Answer 1

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$\it\huge\mathfrak\red{Hello}$]

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√6
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$\it\huge\mathfrak\red{thanks}$]

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Answer 2

let us suppose that root6 is rational number. Then,√6=p/q,where p and q are co-prime and q=not equal to 0.
squaring both the sides,we get
6=p square/q square
6q square=p square
p square is divisible by 6.
so,p is also divisible by 6.
let p=6m for some integer m.
substituting p=6m in (1), we get
6q square=(6m) square=36m square
q square=6m square
q square is also divisible by 6.
so,q is also divisible by 6.
since p and q both are divisible by 6, therefore
6 is a common factor of both p and q . but, this contradicts the assumption that p and q are co-prime.
This is because of our contradictory assumption that√6 is a rational number.
hence,√6 is irrational number.