In particular, for example, what integers $z,y$ are such that $\sqrt 2 + 3 \sqrt{25} = z\sqrt{y}$? ( I mean $25^{1/3}$)
Can this always be done for any expression on the lefthand side, for integers and the operations $+,-,*,/,$ and $√$ ?
Is there a procedure for turning any expression into $y^{1/z}$ ?
Not all irrational numbers can be expressed as $y^{\frac{1}{z}}$ for $y, z $ integers. If an irrational number can be expressed in this way, it would mean that it is an algebraic number. Not all irrationals are algebraic. For example $\pi.$