Solve $\sqrt{x+16}+\sqrt[4]{x+16}=12$.

Solve $\sqrt{x+16}+\sqrt[4]{x+16}=12$.

For some students, they would think to square the given equation three times to get rid of the fourth root and square root terms:

$\sqrt{x+16}+\sqrt[4]{x+16}=12$

$(\sqrt[4]{x+16})^2=(12-\sqrt{x+16})^2$

$\sqrt{x+16}=144-24\sqrt{x+16}+x+16$