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You can certainly make all rational and all irrational roots. I am not sure if you can make transcendental numbers, such as e or pi. I think not.

For example, to make ANY integer, X, you can always find another pair of integers p and q such that 5p + 7q = X.

If you can make one integer, you can make two of them. Divide one by the other and you have all rational numbers.

Make a third integer and you can make an irrational root of a rational number, etc.

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