Prove that 5 minus root 3 whole square is irrational
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Let (root 3 + root 5)2 be of the form a/b where a and b are co-primes and b is not equal to zero. Here the RHS is rational while the LHS is irrational. This is not possible and therefore contradicts our assumption that (root 3 + root 5)2 is rational. Therefore (root 3 + root 5)2 is irrational.
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