Question

How do you simplify `5sqrt5 * 3sqrt3`?

Answer 1

You can write:
`5*3*sqrt(5*3)=15sqrt(15)`

Answer 2

Suppose we start with a simpler problem. What is
`5a * 3b`?

What this really means is
`5 xx a xx 3 xx b`
which can be rewritten as
`5 xx 3 xx a xx b`
`= 15 (a xx b)`

Since in your original question
`a = sqrt(5)` and `b = sqrt(3)`
we only need to know that
in general `sqrt(p) xx sqrt(q) = sqrt(pq)`
or in particular that
`sqrt(5) xx sqrt(3) = sqrt(15)`

So
`5sqrt(5)*3sqrt(3) = 15sqrt(15)`