Question

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.

Answer 1

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.