This week we learned about radicals in expressions, and adding/subtracting them or multiplying/dividing them.

Adding:

When adding radicals there are a few key things to know:

-The only thing that changes is the coefficient.

-The index and the radicand must be the same.

So for example: 2 \sqrt{6} + 4 \sqrt{6} = 6 \sqrt{6}

Subtracting: 

The rules for subtracting are exactly the same as adding since they are inverse operations.

Here’s an example: 14 \sqrt{7} - 9 \sqrt{7} = 5 \sqrt{7}

Multiplying:

For multiplying radicals, it’s very simple. Multiply the rational numbers by the rational numbers, and the radicals by the radicals!

Example:

4 \sqrt{2} * 8 \sqrt{9} = 32 \sqrt{18}

Also note you should simplify when possible.

To do this you must find a perfect square that goes into the radicand. In this case the perfect square 9 goes into 18 two times so:

32\sqrt{9*2}

Then you have to square root the perfect square (9), and then multiply it by the coefficient (36):

32*3\sqrt{2}

Your final answer would then be 96\sqrt{2}

Dividing:

For dividing it goes the same, except you can never have a radical or negative number on the denominator.

If you are dealing with a binomial in the denominator you would then multiply the numerator and the denominator by the conjugate (which is technically equal to one):

\frac{1}{6\sqrt{3}}

 

\frac{1}{6\sqrt{3}}*\frac{6\sqrt{3}}{6\sqrt{3}}

 

\frac{6\sqrt{3}}{36\sqrt{9}}

 

\frac{6\sqrt{3}}{36*3}

 

\frac{6\sqrt{3}}{108}

At this point recognize that 108 and 6 can both be divided by 6, so you can simplify to get your final answer:

\frac{1\sqrt{3}}{18}