To solve the equation sin(2x) * √(cos(x)) = 0, we need to find the values of x that make the equation true.

Firstly, we observe that the product of sin(2x) and √(cos(x)) will be equal to 0 if either sin(2x) = 0 or √(cos(x)) = 0.

sin(2x) = 0
We know that sin(2x) = 0 when 2x is a multiple of π, i.e., 2x = nπ where n is an integer.
Therefore, x = nπ/2 where n is an integer.

√(cos(x)) = 0
This implies that cos(x) = 0, which occurs when x = (2n+1)π/2 where n is an integer.

So the solutions to the equation sin(2x) * √(cos(x)) = 0 are x = nπ/2 or x = (2n+1)π/2 for any integer n.