Question

How do you simplify `root5(-1988)`?

Answer 1

`root(5)(-1988) = -root(5)(1988)` cannot be simplified further.

Explanation:

Factoring `1988` into prime factors we find:

`1988=2*2*7*71`

Since this has no factors with `5`th powers, there is no positive factor we can "move outside" the radical.

However, we do know `(-1)^5 = -1`, so it is possible to move the minus sign (i.e. factor `-1`) outside of the radical.

Spelled out we have:

`root(5)(-1988) = root(5)((-1)^5 * 1988) = root(5)(-1)*root(5)(1988) = -1*root(5)(1988) = -root(5)(1988)`