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)

Answer:

The expression sqrt (-18x ^ 3y ^ 4) is equivalent to:

3 * x * y ^ 2 * i * sqrt (2x)