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>> Julie Harland: Hi.
This is Julie Harland,
and I'm your math gal.
Please visit my website
at yourmathgal dot com
where you can search for any
of my videos organized
by topic.
This is part 12B
of square roots and radicals,
and we do the following two
problems on this video.
Alright. We're going
to simplify this problem.
So right now,
the variable part
with the cube root is not the
same on each of them.
So they don't look
like like terms at all.
So what we're going
to do is begin
by simplifying each
term separately.
Alright. So in the first one,
we want to see
if there's any perfect cube
in here.
So for 24,
the question is is there a
factor of 24 that's a
perfect cube.
So you need
to know your perfect cubes.
Two cubed is 8, 3 cubed is 27,
4 cubed is 64,
etc. and 8 goes into 24.
So I could write this
as 8 times 3.
Eight's a perfect cube.
Now that's different
than when you're looking
with variables and exponents.
So when you take the cube root
of something
that has an exponent,
you're looking for an exponent
that 3 goes into.
If it's a cube root,
you want the exponent to be,
in other words,
a multiple of 3.
Three, 6, 9.
So x cube fits the
bill already.
So I can leave it like that.
So the cube root
of 8 I could take out as 2.
Notice this number here isn't
a number that 3 goes into.
I'm actually,
this is a co-efficient inside
here, right.
So you're looking
for a number that's a perfect
cube, but x cubed you're
looking for the exponent
to be a multiple of 3.
It's a little tricky.
So the cube root
of x cube then is x. The new
exponent will just be 3
divides into 3 1,
or you should know
that cube root of x cubed is 3
because if it's an odd
exponent, cube root
of something [inaudible].
Let's see the fourth root of x
to the fourth is x,
the fifth root of x
to the fifth is x,
etc. Alright.
Let's go on to the next one.
You've got to see
if there's a perfect cube
that is a factor of 81,
and we'll [inaudible] 8 is the
first perfect cube, right.
That doesn't go into 81.
The next one is 3 cube, 27,
and that does go into 81.
So we have 27 times 3.
And now we're looking
for an exponent, right,
that 3 goes into evenly,
and 3 does not go
into 4, right.
So we have to go down.
What's the number below 4
that 3 goes into?
That would be 3.
So we want to rewrite
that as y cubed times y.
So my perfect cube's
over here, or the cube root
of 27, which is 3,
and the cube root
of y cube is y.
So whatever we pull
out gets multiplied
by anything in the front.
So I have 5y times 2 times x.
That'll give me a 10xy,
and what's left inside is just
the 3y.
For my next term,
I have 4x times 3 times y.
So that's, 4 times 3 is 12xy,
and what's left inside is
a 3y.
So I have a cube root of 3xy.
Now I'm going to look and see
if these are like terms.
So the like terms are exactly
the same here.
They both are xy cube root
of 3y.
They have to be exactly
the same.
If you had a y square inside
and a y over here,
it's not going to work.
If I only had an x
out in front,
not an xy over here,
that would not work.
But these are really right
here exactly the same
like terms.
So this is just
like doing 10m minus 12m.
You would have negative 2m.
You just subtract 10 minus 12.
So that's a negative 2,
and then you just write the
variable part.
So you write that whole thing,
and that is your answer.
[ Pause ]
>> Julie Harland:
Here's our next problem we're
going to simplify.
Now I might kind of run
out of space
since I'm writing this,
but let's just try it.
So for this first one,
I'm looking to see
if underneath here I've got,
I can write this
as some perfect cubes,
and notice the x
to the 6 is already perfect
cube, but this 54 is a
little problem.
So I'm going
to just write underneath here.
That's 27 times 2,
and I'm going to rewrite
that y to the fifth
as y cubed times y squared.
So they're perfect cubes.
So then what can I really, so,
in other words, instead of 54,
I'm going to think of that
as 27 times 2.
Instead of y to the fifth,
I'll think of that
as y cubed times y. So now,
the cube root of 27 is 3.
I can take that out.
X to the 6 is a perfect cube
because the exponent is a
number that 3 goes into.
Three goes into 6.
So this will be x squared.
OK. And then y cubed,
cube root of y cubed is y.
So it's a little bit messy,
but I just was going to run
out of space unless I kind
of did it like that.
So what do I have
if I rewrite what this
simplifies to?
I've got 2 times 3 times x
squared times y.
So I've got 6x squared y
cube root.
Alright. Now what's left
in here?
Be careful.
You've got what's left.
I've got that 2
and that y square.
So I've got 2y square.
So that's the first term.
Plus. Alright.
Now let's simplify this one
over here.
Well, I can't take anything
out of this 2y square
in the middle.
So that's nice.
I just get to keep that.
Three x squared y cube root
of 2y squared.
What about this last one?
Let's see.
Do I have a perfect cube
in here?
Well, 8 goes into 16.
So I'm just going
to say that's the same
as 8 times 2,
and then x cube is already a
perfect cube.
So out of this 8,
I can take out a 2,
cube root of 8,
and out of the x cube,
I could take out an x.
So that gets multiplied
by what's out in front.
So I have x times y times 2
times x. So that's 2x
square y.
[ Pause ]
>> Julie Harland:
And what's left is I have a 2
and a y square.
OK. Again, nice.
So, wow. Now we look and see.
Do we have like terms here?
So for this first one,
I've got x square y cube root
of 2y square.
In fact, let's see.
If I highlight this,
it might be even easier
to see.
Look at the variable part
with the radicals.
It's exactly the same.
So all I do is add
the co-efficient.
Six plus 3 minus 2.
So that's 9 minus 2, that's 7,
and then you just write the
variable part down.
X square y cube root
of 2 y square.
So it's kind of a doozy.
A little more complicated
than some problems,
but at least this second one
it was already simplified,
but just keep in mind.
Unless the variable part
with the radicals like,
has to be exactly the same.
These have
to look exactly the same
in order to combine
like terms.
[ Pause ]
>> Julie Harland:
Please visit my website
at yourmathgal dot com
where you can view all
of my videos
which are organized by topic.