To rationalize the denominator of the given expression, 4√3 5√2 ÷ √48 √18, we need to eliminate any square roots in the denominator by multiplying both the numerator and denominator by a suitable expression.

Here's how you can rationalize the denominator step by step:

Step 1: Simplify the expression

We can start by simplifying the expression to make it easier to work with:

4√3 5√2 ÷ √48 √18

Step 2: Simplify the square roots

We can simplify the square roots in the expression:

√48 = √(16 * 3) = 4√3
√18 = √(9 * 2) = 3√2

So, the expression becomes:

4√3 5√2 ÷ 4√3 3√2

Step 3: Rationalize the denominator

To rationalize the denominator, we need to eliminate the square roots in the denominator by multiplying both the numerator and denominator by the conjugate of the denominator.

The conjugate of the denominator, √48 √18, is √48 - √18.

So, we can multiply both the numerator and denominator by √48 - √18:

(4√3 5√2) * (√48 - √18) / (4√3 3√2) * (√48 - √18)

Now, let's simplify the expression:

(20√6 - 5√6) / (12√6 - 9√6)

We can see that the √6 terms in both the numerator and denominator cancel out:

(20 - 5) / (12 - 9)

Simplifying further, we get:

15 / 3 = 5

So, the rationalized form of the given expression is 5.

Therefore, the denominator of the expression 4√3 5√2 ÷ √48 √18 is rationalized to become 5.