Absolute values are very easy and straightforward. They describe how far a number is from the zero point on the number line. In this fashion, they will always be positive (unless the negative sits on the outside). Example:

|-5| = 5

They function very similarly to normal parenthesis. The only difference is you cannot distribute them. Example:

5|14-3| –> 5|11| = 55

This is a simplified version of the possibilities of absolute values. Still anything else you’d put inside would show the exact same theory, albeit harder algebra ect.

Now on to radicals. In week 3 we learned our basics of radicals and how to simplify them. If you are lucky and the radicand is a perfect square/cube/what have you, then solve for the whole number. However often the radical is irrational and to simplify these, we must factor. Taking the list of perfect squares 4,9,16,25,36,49,64,81,100,121,144 you see which number from this list goes into your radicand and split it into a multiplication. For example 28 is the same as 7*4. From here you take the perfect square and remove it from the radical, thereby rooting it and turning it into a coefficient. Our 4 would turn into a 2. Here is an example on simplifying a radical now.

5√32 =

5√8*4 =

5*2√8 =

10√8