I need help on the procedure and rules for these kinds of problems. Here are two examples from my book.
(*=radical sign)
*2 (*2 + *3)
*3(*15 + *21)
$\displaystyle \sqrt{2} \left(\sqrt{2} + \sqrt{3}\right)$
Just imagine $\displaystyle a = \sqrt{2}, b=\sqrt{3}$. This gives you: $\displaystyle a(a+b)$ which is something you probably know how to do already.
Just keep in mind that when multiplying two radicals, you can combine the numbers under it and put it under a single radical, i.e. $\displaystyle \sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$
$\displaystyle \sqrt{3}\left(\sqrt{15} + \sqrt{21}\right)$
Try the same thing as above.
Distribute like you would any other number, and then use this property to simplify: $\displaystyle \sqrt{a}\sqrt{b} = \sqrt{ab}$, where $\displaystyle a,\ b$ are nonnegative real numbers. Here is an example of the basic process:
$\displaystyle \sqrt{5}\left(\sqrt{5} - \sqrt{2}\right)$
$\displaystyle = \sqrt{5}\sqrt{5} - \sqrt{5}\sqrt{2}$
$\displaystyle = \sqrt{5\cdot5} - \sqrt{5\cdot2}$
$\displaystyle = \sqrt{25} - \sqrt{10}$
$\displaystyle = 5 - \sqrt{10}$