Question

How do you multiply the radicals `5sqrt2 * 8sqrt2`?

Answer 1

Remember that multiplications can be reordered and regrouped as we like. So

`5sqrt2*8sqrt2=5*8*sqrt2*sqrt2=40*2=80`

In case it is not clear `sqrt2*sqrt2 = 2` because that's how square root is defined.
Alternatively: `sqrt2*sqrt2=sqrt(2*2)=sqrt4=2`