15.4. Solve for $x: 16^{1 / 8}+x^{1 / 4}=\frac{23}{5-\sqrt{2}}$.
15.4. 625
After rationalizing the denominator, we get
$$
16^{1 / 8}+x^{1 / 4}=5+\sqrt{2} \text {. }
$$

It follows that $x^{1 / 4}=5$ or $x=625$.