given a decimal expansion

$$ 0.345345345... $$

then we can recover the fraction from this decimal expansion , in this case $ \frac{345}{999} $

my question is if for a non-periodic decimal expansion

$$ 0.451235132535126535126164616146462462 $$ we can find two numbers a and b integers so

$$ a+ \sqrt{b} = 0.451235132535126535126164616146462462 $$ or if there is a theroem which make it an impssible task.