Question

Simplify. Assume that x and y are positive numbers.

√x^3y^3

A. xy√xy
B. x²y²√xy
C. xy√x²y²
D. xy

Answer 1

To simplify the expression √x^3y^3, factor out the square root of each variable raised to the power of 2 and simplify to get xyxy = x^2y^2.

Step-by-step explanation:

To simplify the expression √x^3y^3, we can factor out the square root of each variable raised to the power of 2. Since x^3 = (x^2)(x) and y^3 = (y^2)(y), we can rewrite the expression as √(x^2)(x)(y^2)(y).

Using the property √(ab) = √a √b, we can separate the square root into two parts and simplify further to get (x)(y)√(x^2)(y^2). This can be written as xy√(x^2y^2).

Simplifying further, we know that √(x^2) = x and √(y^2) = y, so the final simplified expression is xyxy = x^2y^2.