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

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 ?

anonymous · Answer

sqrt(25)  can be either +5 or -5 because  
+5 * +5 = 25   and   -5 * -5 = 25

sqrt(-25) this cannot exist under the real numbers because there is nothing times itself that is going to give you a negative number because a positive times a positive is a positive and a negative times a negative is a positive.

cuberoot(27) cannot have a positive and a negative.  In this case there is only 1  and that is 3  because 3 * 3 * 3 = 27

if you had the cuberoot(-27) cannot have a positive and a negative.  In this is case there is only 1 and that is -3 because -3 * -3 * -3 = -27