The expression sqrt(-18x^3y^4), where x and y both are greater than zero, is equivalent to

We have the following expression:
 sqrt (-18x ^ 3y ^ 4)
 Let's rewrite the expression:
 sqrt (-2 * 9 * x * x ^ 2 * y ^ 4)
 (-2 * 9 * x * x ^ 2 * y ^ 4) ^ (1/2)
 ((-2 ^ (1/2)) * (9 ^ (1/2)) * (x ^ (1/2)) * (x ^ 2 ^ (1/2)) * (y ^ 4 ^ ( 1/2)))
 ((-2 ^ (1/2)) * (3) * (x ^ (1/2)) * (x ^ (2/2)) * (y ^ (4/2)))
 ((-2 ^ (1/2)) * (3) * (x ^ (1/2)) * (x) * (y ^ 2))
 3 * x * y ^ 2 * ((- 2 ^ (1/2)) * (x ^ (1/2)))
 3 * x * y ^ 2 * (- 2x) ^ (1/2)
 3 * x * y ^ 2 * i * (2x) ^ (1/2)
 3 * x * y ^ 2 * i * sqrt (2x)
 
 The expression sqrt (-18x ^ 3y ^ 4) is equivalent to:
 3 * x * y ^ 2 * i * sqrt (2x)

Wow. that is a really cool question.