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there is no cube roots in negative
The short answer is "Nothing". In the complex domain, the number of nth roots of any real number is n. Every non-negative real number has 2 square roots. Every real number has 3 cube roots. Every non-negative real number has 2 real square roots and 2 imaginary ones. and so on. So what?
For a pure imaginary number: {i = sqrt(-1)} times a real coefficient {r}, you have i*r. The cube_root(i*r) = cube_root(i)*cube_root(r), so find the cube root of r in the normal way, then we just need to find the cube root of i. For any cubic function (which has a polynomial, in which the highest term is x3) will always have 3 roots. There are 3 values, which when cubed will equal the imaginary number i:-i will do it: (-i)3 = (-i)2 * (-i) = -1 * (-i) = iThe other two are complex: sqrt(3)/2 + i/2 and -sqrt(3)/2 + i/2If you cube either of the two complex binomials by multiplying out, you will end up with 0 + i as the answer in both cases.Note: the possible roots for any cubic are: 3 real roots, or 1 real root and 2 complex root, or 1 pure imaginary root, and 2 complex roots.For your original question, if you want to stay in the pure imaginary domain, then you can use: Cube_root(i*r) = -i * cube_root(r) to find an answer.
All numbers have cube roots (not necessarily integral cube roots) so every prime has cube roots.
Yes.
There are 3 cube roots of 27. There are 2 square roots of 27 ( or any real number ). There are 4 fourth roots of 27 and so on:)
Many calculators will offer a way for you to do cube roots, or what number to the power of 3 will equal that number. There is no easy way to go about finding cube roots without a calculator, so I suggest not trying too hard.. but the cube root of 7 is 1.912931182772389 found from using a simple Cube Root calculator you can find on the internet.
There is no number that has more than two square roots.By definition, the "square" bit implies two.Every number has exactly:TWO square roots,THREE cube roots,FOUR quadratic roots,etc.
you are my friend
Every number between 50 and 70 is a cube. For example, 53 is the cube of the cube root of 53 = 3.7563 (approx).The perfect cube roots in the range is 64.
I posted an answer about cube roots of complex numbers. The same info can be applied to square roots. (see related links)