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

1 Answer
Aug 13, 2016

Answer:

#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)#