Question

Please explain how to simplify:
sqrt(16c^8)-sqrt(c^2)+2*sqrt(c^2)+sqrt(4c^2).

Answer 1

Remember that:
\[\LARGE \sqrt{x}*\sqrt{x}=x\]

Answer 2

So \[\LARGE \sqrt{c^2}*\sqrt{c^2}=c^2\]

Answer 3

that makes sense, like sqrt(25)*sqrt(25)=5?

Answer 4

But how do I add and subtract them?

Answer 5

\(\large \bf \sqrt{16c^8}-\sqrt{c^2}\times \sqrt{c^2}+\sqrt{4c^2}\quad ?\)

Answer 6

no, that would equal 25.
Well, once you simplify them, if they have the same thing inside, then you can perform the indicated operation. So say we have:
\[\LARGE 3\sqrt{x}+5\sqrt{x}\]
We can add them because they both have that x.
So it would just be \[\LARGE 8\sqrt{x}\]

Answer 7

Close but not quite, \[\sqrt{16c^8}-\sqrt{c^2}+2\sqrt{c^2}+\sqrt4c^2\]

Answer 8

Okay.

Answer 9

That makes sense.

Answer 10

So simplify the remaining two.

Answer 11

Ok, just a sec.

Answer 12

Sorry, I'm a little confused which two do you want me to simplify?

Answer 13

The \[\LARGE \sqrt{16c^8}\] and \[\LARGE \sqrt{4c^2}\]

Answer 14

Oh, ok.

Answer 15

\[\sqrt{20c^10}\]

Answer 16

Ummm
That one zero thing should be a ten.

Answer 17

Not exactly.

Answer 18

Oh.

Answer 19

So what did I do wrong?

Answer 20

Hello?

Answer 21

Sorry about that, but here:
\[\LARGE \sqrt{4*4c^8}-c^2+\sqrt{2*2c^2}\]
Simplified:
\[\LARGE 4c^4-c^2+2c\]

Answer 22

Hmm, Okay, I think that makes sense. However, the third term should have been \[2\sqrt{c^2}\] not \[c^2\], or maybe I'm just confusing my self, lol.

Answer 23

No, it's c, because if we break it up:
\[\LARGE \sqrt{c*c}\] and you know what that means?

Answer 24

\[\LARGE \sqrt{c}*\sqrt{c}\] is another way of writing it.

Answer 25

No I didn't understand that, but I think that makes sense.

Answer 26

hmm, ok now I get it.

Answer 27

Sorry I'm not very quick at this.

Answer 28

It's alright.

Answer 29

So, if I want to simplify sqrt(4c^2) it would look like 2*2c^2?

Answer 30

Breaking apart you mean?

Answer 31

*it apart

Answer 32

Yes.

Answer 33

Well if you want to go down to the simplest:
\[\LARGE \sqrt{2*2*c*c}\]

Answer 34

Ok, that makes sense. Now what?

Answer 35

If there's 2 of the same things, you can take them out as one, so the 2 and c's are the same:
\[\LARGE \sqrt{\color{red}{2*2}*\color{green}{c*c}}=\color{red}{2}*\color{green}{c}\]

Answer 36

Okay.

Answer 37

So I have:\[4c^4-c^2+2c\] now?

Answer 38

oops

Answer 39

I meant:

Answer 40

\[4c^4-c^2+2c+2c\]

Answer 41

Well, since none of them have the same exponents, you just leave it as it is. So \[\LARGE 4c^4-c^2+2c\]Will be your answer

Answer 42

Because I can't combine like terms, right?

Answer 43

Exactly.

Answer 44

Great, thank you so much for your help. :)

Answer 45

I understand a lot better now.

Answer 46

Anytime bud~