Algebra
posted by Taurus on .
I need help on these kinds of radical problems. Once I get the examples solved, I think I can do others.
1. What is the solution to the square root of 9? No solution, yes or no?
2. The square root of: 6x/3x? The answer is 2?
3. The square root of 0.01? No solution? Is there an answer to the square root of a negative number?
4. The cube root of 3 times the cube root of 9.

3 i or 3 times the square root of 1
If you have not had imaginary numbers in your course, the answer is no real number solution
no, square root of 2 or [ sqrt 2 }
Yes there is an answer to the square root of a negative number but not in real numbers. If you have not covered imaginary and complex numbers, then there is no solution.
(27)^1/3
This is not imaginary but complex, a sum of real and imaginary parts.
convert to polar coordinates in the complex plane
27 (cos 180 + i sin 180)
or
27 e^(180 i)
now take cube root by finding cube root of coef and dividing theta by 3
3 e^60 i is a root
so is 3 e^(60+120)i and 3e^(60 120 i) or 3 ( cos 60 + i sin 60)
3 (cos 180 + i sin 180)
3(cos 60 + i sin 60)
3 ( .5 + .866 i)
3
3 ( .5  .866 i)
If you do not know complex numbers, 3 is the only answer you can give.