Question

What is the simplified form of √(25x^2y^2) / √(xy) assuming x > 0 and y > 0?

Answer 1

The simplified form of √(25x^2y^2) / √(xy) is 5xy.

Step-by-step explanation:

The simplified form of √(25x^2y^2) / √(xy) is 5xy.

To simplify this expression, we can write the square roots as fractional powers. So, √(25x^2y^2) can be written as (25x^2y^2)^(1/2), and √(xy) can be written as (xy)^(1/2).

Now, when we divide these two expressions, we subtract the exponents: (25x^2y^2)^(1/2) / (xy)^(1/2) = (25x^2y^2 - xy)^(1/2).

By simplifying the expression inside the square root, we get (25x^2y^2 - xy)^(1/2) = 5xy.