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

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Answer 1 · 2016-08-13T07:30:11

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

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:

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

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