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Let us assume that (2+2(3^(1/2)))^1/2 is an irrational number.
it can be expressed as p/q where p,q have no common factors and are rational numbers.
squaring both sides, we have,
1+3^(1/2)= p^2/2(q^2)
3^1/2= p^2-2q^2/2q^2
we see that rhs is a rational number but lhs is irrational.
this is a contradiction.
hence, the given number is irrational.
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