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

Odds are when you try to do (-1)^1/2 you're getting (-1)^1/3, as it's a strange coincidence that you're getting the cube root of -1. -1 x -1 x -1 = -1.

Either you're accidentally clicking on 3 and getting 1/3 for the power instead of 1/2 or the calculator itself is mistaking a 2 for a 3.

Maybe try taking (8)^1/2 and see if it gives you 2.8 or 2. If it gives you 2, then it's giving you the cube root.

You should be getting "error" either way.

maybe when you clicked on -1 you didn't hit the - hard enough?

sqr(-1) is i, not -1. i is an imaginary number, not a real number that would show up on a calculator

sqr(1) is 1 although -sqr(1) = -1

so you shouldn't be getting -1 no matter what you clicked on

by the way the calculator only gives positive square roots and only real roots.

when it gives you the cube root of -1 as -1, that's a real root, and the calculator doesn't give you the other two cube roots which are imaginary. solve x^3 + 1 = 0 and you get 3 solutions, all cube roots of -1

factor it to get (x+1)(x^-x+1)=0 set the factors = 0 and you get, -1, and also 1/2 + or - isqr3