(-16)^1/2 is equal to -16^1/2???

Question

i cannot understand d difference

wat can be d best solution??

Answer 1

( 16 i ² )^(1/2) = ± 4 i

Answer 2

no way

Answer 3

It is not equal,

-(16)^1/2 = 4i

& -16^1/2 = -4

Any number raised to 1/2 means that you are taking square root of that number. Also, while evaluating any mathematical expression you have to follow a sequence.

Here in the second expression,  square roots should be evaluated first & after that the -ve sign. Thus, you should first find out the square root of 16, which is 4 & in the next step attach the -ve sign to it.

In the 2nd expression, since -ve sign is inside bracket it is evaluated first & you should take the square root of -16 as a whole. Which is 4 multiplied by the imaginary number 'i' which is the square root of (-1).

Answer 4

(-16)^(1/2) is the number -12 squared, and equals 4i, where i^2=-1

-16^(1/2) is the negative of 16^(1/2) and is equal  =4

Answer 5

inn the set of real numers, you cannot have a sqrt out of a negative number.

therefor, in R, sqrt( -16)  does not exist.

in the complex set, -16 = 16 *i ^2 = (4i)^2 and sqrt(-16)= 4.

the second one is just - sqrt( 16)  = - 4

Answer 6

the first one is unreal (it is complex number since the negative is under the root)

the second one is real (the negative is not under the root), you can solve it (the result is -4).