Example

Solve for $w$: $\quad \sqrt[4]{w}=-4$

Solution

This equation involves a fourth root---a radical with an even number index. Even-indexed radicals only describe nonnegative numbers. $\sqrt[4]{w}$ cannot possibly be equal to a negative number. There is no solution.

Warning: if you would have "solved" this equation raising both sides to the 4th power, you would have found a "solution". That solution would not have checked out when substituted back into the original equation.

Compare this example with Example 16.