To rationalize the denominator of the given expression, let's start by simplifying the expression first.

Given expression: (4√3 * 5√2) / (√48 * √18)

Let's simplify the numerator first, which is the product of 4√3 and 5√2.

Numerator: 4√3 * 5√2 = 20√6

Now, let's simplify the denominator, which is the product of √48 and √18.

Denominator: √48 * √18

To simplify this, we can break down the square roots of 48 and 18 into their prime factors.

√48 = √(2^4 * 3) = 2^2 * √3 = 4√3

√18 = √(2 * 3^2) = 3√2

Now, we can substitute the simplified values back into the expression:

Expression: (20√6) / (4√3 * 3√2)

Now, let's simplify the expression further by canceling out common factors.

Expression: (20√6) / (4 * 3 * √3 * √2)

= (20√6) / (12√6)

= 20/12

= 5/3

Now, the expression has been simplified to 5/3, and the denominator is already rationalized.

To summarize:

Given expression: (4√3 * 5√2) / (√48 * √18)

Simplified expression: 5/3

Thus, the rationalized form of the given expression is 5/3.