State the restrictions on the variables and then simplify each of the following expressions.

Question

A.) X root 12x^4
The answe is 2x^3 root 3 but I don't know how to get the answer it.
B.) (3x root x^2)(2 root x^5)
The answer is 6x^4 root X but I don't know how to get the answer.
Consider the equation -7= 2- root 12x-3. Solve the equation. The answer is X=7 but I can't figure out how to get the answer.

Answer 1

x√(12x^4) = x√(4x^4*3) = x(2x^2)√3 = 2x^3√3

3x√x^2 * 2√x^5 = 6x√(x^2*x^5) = 6x√(x^6 * x) = 6x*x^3 √x = 6x^4 √x

-7 = 2-√(12x-3)
-9 = -√(12x-3)
81 = 12x-3
84 = 12x
x = 7