# Week 4 – precalculus 11

To multiply a radical expression you want to use strategies such as distributive property. This may involve adding radicals too, to add a radical the radicand has to be the same and you will add the coefficients together. When multiplying all we need to do is multiply the coefficients together and the radicand. The radicands need not match. For example

$4\sqrt{3}$ x $3\sqrt{2}$

Would equal… (After you multiply the respective coefficients and radicands together)

$12\sqrt{6}$

In a situation where there is one radical outside of brackets that contain two radicals that are adding or subtracting, we want to distribute. Multiply each radical on the inside by the one on the outside. For example

$\sqrt {6} (4\sqrt{3}+3\sqrt{2})$

You would multiply each radical by six

$4\sqrt{18} + 3\sqrt{12}$

And simplify

$4\sqrt{9}X{2} + 3\sqrt{3}X{4}$

Then multiply the coefficient by the new perfect squares (In this case 3 and 2)

$12\sqrt{2} + 6\sqrt{12}$

You can even multiply $( \sqrt {3} + 2) (\sqrt {3} - 2)$

To do this we will have to FOIL. This means we will multiply the first value in the first bracket by both of the values in the second bracket and we will do the same with the second value in the first bracket. This will give us four numbers that are to be added or subtracted the brackets will now be gone.

$\sqrt{9} - 2\sqrt{3}+2\sqrt{3} - 4$

The negative and positive $2\sqrt{3}$ cancel out. And we are left with…

$\sqrt{9} - 4$

9 has a perfect square of 3 so,

$3 - 4 = -1$

This is how to multiply Radicals based on what the format of the equation is.