how do you multiply a radical with a regular number ? for example:

4radical2 ( 2+ 2radical3)

first term:
4sqrt2 * 2= 8sqrt2
second term
2sqrt2 * 2 sqrt3= 2*2 * sqrt (2*3)
= 4 sqrt6

first term:
4sqrt2 * 2= 8sqrt2
second term
2sqrt2 * 2 sqrt3= 2*2 * sqrt (2*3)
= 4 sqrt6

To multiply a radical with a regular number, you can follow these steps:

Step 1: Multiply the regular number with the number outside the radical.
In your example, 4√2 * 2 = 8√2.

Step 2: Multiply the numbers inside the radicals.
In your example, 2√2 * 2√3 = 2 * 2 * √(2 * 3) = 4√6.

So, when you multiply 4√2 with (2 + 2√3), you get 8√2 + 4√6.