Give me the next problem you are having trouble with, and I'll work through it here.
😉
Double Post (next time use the edit button!):
Here's one just for kicks:
radical a x radical ab
Ok, so we cant touch radical (a) yet. Nothing we can do with that part, so let's move on.
Radical (ab): Ok, here we can split it up. Right now it is
Radical (a times b).
Any time we have two numbers in a radical sign that multiply with one another, we can split them up into seperate radicals. So let's change that into Radical(a) x Radical(b), instead of Radical (ab).
So let's look at what we got so far:
Radical (a) x Radical (a) x Radical (b)
-now any time you have a radical multiplied by an identical radical, you can just delete those radicals, and keep only the number inside. For instance:
Radical (4) x Radical (4) (but hey! The square root of 4 = 2, so Radical (4) = 2.)
=2 x 2
=4
This is just to show you why it always works.
So to continue:
Radical (a) x Radical (a) x Radical (b)
becomes
a x Radical (b)
_____________
radical (8bc) x radical (4bc)
again, the first step is to split everything up. Let's write each multiplied number in the radicals, as their own seperate radical
radical (8) x Radical (b) x Radical (c) x Radical (4) x Radical (b) x Radical (c)
Put the Radicals that are the same together to make it easier to see
radical (8) x radical (4) x radical (b) x radical (b) x radical (c) x radical (c)
But remember what happens when you multiply one radical by another identical radical? They cancel, leaving only the number inside remaining. So...
radical (8) x radical (4) x b x c
next step: We can see that Radical 4 is easy. The square root of 4 = 2. So let's write that in
radical (8) x 2 x b x c
now we have that nasty 8. Let's break it up, so that one of the numbers inside the radical is a perfect square
radical (4x2) x 2 x b x c
split up the radical. Numbers multiplied inside a radical can be made into two seperate radicals instead
radical (4) x radical (2) x 2 x b x c
again, 4 is a perfect square, so the square root of 4, is 2.
2 x radical (2) x 2 x b x c
multiply the two whole numbers (integers) together
2 x 2 x radical (2) x b x c
4 x radical (2) x b x c
might as well make it look pretty
4bc x radical (2)
done!~