# Thread: Radical times two other radicals(distributive property)

1. ## Radical times two other radicals(distributive property)

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)

2. $\sqrt{2} \left(\sqrt{2} + \sqrt{3}\right)$
Just imagine $a = \sqrt{2}, b=\sqrt{3}$. This gives you: $a(a+b)$ 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. $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$

$\sqrt{3}\left(\sqrt{15} + \sqrt{21}\right)$

Try the same thing as above.

3. Originally Posted by endlesst0m
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)
Distribute like you would any other number, and then use this property to simplify: $\sqrt{a}\sqrt{b} = \sqrt{ab}$, where $a,\ b$ are nonnegative real numbers. Here is an example of the basic process:

$\sqrt{5}\left(\sqrt{5} - \sqrt{2}\right)$

$= \sqrt{5}\sqrt{5} - \sqrt{5}\sqrt{2}$

$= \sqrt{5\cdot5} - \sqrt{5\cdot2}$

$= \sqrt{25} - \sqrt{10}$

$= 5 - \sqrt{10}$