Why it shows me Error when calculating sqrt (-1) ?

Question

When I calculate the value of (-1)^1/2 the answer is -1

but when I do the same thing but with radical √-1 the answer is error ?!!

since the radical √ is to the exponent to 1/2 in case of square root not others with higher indexes why the answer is not the same ?!

Answer 1

The answer to (-1)^{1/2} can not be -1 as you say. To see this just multiply -1 with itself and you get 1, not -1. You can not put a negative real number under a square root and expect the result to be a real number. That is why we invented imaginary numbers.