For people good at Algebra, my friend asked and I wasn't sure so I told her I would post it for her. Lets assume that the radicand is a positive number.

If the index is 2, can we have two roots, one positive and one negative? If yes, illustrate with an example. If not, why not ? What if index = 3 ?

Question

For people good at Algebra, my friend asked and I wasn't sure so I told her I would post it for her. Lets assume that the radicand is a positive number.

If the index is 2, can we have two roots, one positive and one negative? If yes, illustrate with an example. If not, why not ? What if index = 3 ?

dumbcow · Answer

If x^2 = 4, then x = +-sqrt(4) = +-2
--> 2^2 = 4,  and (-2)^2 = 4

If x^3 = 8, then x = cuberoot(8) = 2
--> 2^3 = 8 ,  but (-2)^3 = -8

So if index is 2, there are 2 solutions one pos, one neg
If index is 3, there is only 1 solution