Question

Any good with Trignometry? Please help with this problem:

Answer 1

Heres the problem: \[(\sqrt[3]{x+1})^{3}-1\]

Answer 2

Where's the trig?

Answer 3

Its above.

Answer 4

Unless I'm missing something, the answer's "x".

Answer 5

haha, that is the answer. But I'm trying to figure out how to get to that answer.

Answer 6

How so?

Answer 7

Idk. I don't really understand how to solve it.

Answer 8

Well, you're just cubing the cubed root of "x+1", which gets you back to where you started (i.e. "x+1"). And then you subtract "1", leaving you with "x".

Answer 9

but ... you have an index. =\

Answer 10

Well ... the root.

Answer 11

Thats what killed me.

Answer 12

What's confusing you?

Answer 13

The root of 3.

Answer 14

Oh, yeah, that just means "cubed root". To make things easier, you can always convert that to exponents.

Answer 15

So, if you see:
\[\sqrt[3]{x}\]
You can rewrite it as:
\[x ^{\frac{ 1 }{ 3 }}\] i.e. to "x" raised to the one-third power.

Answer 16

Ohhh.

So lets work this out together.

Answer 17

\[\sqrt[3]{(3)^{3}-1}\]

Answer 18

cubed root of 26

Answer 19

Hahaa. WTH? How are you getting that!!!!!
hahaa.

Answer 20

BREAK IT DOWN ... all the way for me man!

Answer 21

If you have a calculator handy you can write:

\[(26)^{\frac{ 1 }{ 3 }}\]

Answer 22

How did you get 26 though.

Answer 23

NVM!

Answer 24

I just did it in my head. (3)^3-1 = 26

Answer 25

Ok so where are we right now? Meaning: what else is a little foggy for you?

Answer 26

Im going to solve this problem:

\[(\sqrt[3]{x+1})^{3}-1\]

Answer 27

Im guessing the answer is just X ?

Answer 28

Yeah, it should be...

Answer 29

Sweet! Im starting to get the hang of this now.

Answer 30

Great! If you have any other questions just ask.

Answer 31

I dont understand how the root comes into the answer and sometimes it cancels out.

For example:

\[(\sqrt[3]{x+1})^3-1 = x\]

BUT :

\[(\sqrt[3]{(3)^3-1} = x\]

= \[(\sqrt[3]{26}\]

Answer 32

Yeah--good question. It's because those two expressions on the lefthand side are NOT equal.

Answer 33

Think of it this way. Actually, just forget about roots for a second.

Is
\[(x+1)^{3}\]
the same as:
\[x^{3}+1\]

Answer 34

Sometimes, the two expressions MIGHT be equal but are they ALWAYS equal? No way!

Answer 35

oooooh. Sweet !

Answer 36

(x+1) ^3 isn't the same as x^3+1

Answer 37

No,
\[(x+1)^{3} = x ^{3}+3x ^{2}+3x+1\]

Answer 38

That's called an IDENTITY because it is always true no matter what value you choose for "x".

Answer 39

And in trig you'll see a lot of Trig IDENTITIES

Answer 40

Oh okay. So that mean that when Im solving the root values, I have to watch out then.

For some reason it feels like i need a little clarification on remembering when and when not to bring down the root.

Answer 41

The identities thing is understandable though.