Question

\[\sqrt[30]{2}\]

Answer 1

And the question is...

Answer 2

How do you solve it? Like put it in decimal form?

Answer 3

Can you use a calculator?

Answer 4

Do you know logarithm?

Answer 5

Yes but it doesn't give me the correct answer. And I would like to know how to solve it. I'm learning Logarithm but I don't really get it..

Answer 6

This is all what logarithm is: [Plus, some properties also!! :D ]

If \(a^b = c\) then this can also be written as: \( \log ~~of ~~{c}~~ to~~ the ~~base ~~a~~ =~~ b\)

Thus, it is another way of representing exponents.

I am not quite sure, if it'll be of any use here though.

Answer 7

Let me just try it once.

Answer 8

Only for curiosity, from which lesson is this problem?

Answer 9

It is just a review for my final but I can't seem to remember how I'm suppose to do this. So the answer to your question is 6.7.31

Answer 10

Ok, I don't know how logartihms can be used to solve this problem, may be they can be useful. Another way is to use the Taylor expansion, something like this,
\[\sqrt[30]{x}\approx 1+\frac{x-1}{30}-\frac{29 (x-1)^2}{1800}\]
or the binomial expansion for a radical ( http://en.wikipedia.org/wiki/Binomial_theorem#Newton.27s_generalised_binomial_theorem).

Answer 11

But I think, the answer must not be so complicated.

Answer 12

I assume you know that the problem can be written as
\[ 2^{\frac{1}{30}} \]
if you take the log (base 10) of this you could write it as
\[ \frac{1}{30} \log(2) \]
if you "undo" the log by making this the exponent of 10
\[ 10^{\frac{1}{30} \log(2) } = 1.023373892 \]

\[ 1.023373892^{30} = 2 \]

Answer 13

None of that really makes much sense, because you need a calculator to do it... so you may as well evaluate 2^(1/30) and get the answer directly.

Answer 14

Yes I think, this should be the best way.

Answer 15

Hahaa! But that was the logarithm approach!

Answer 16

I mean, using the calculator. :)

Answer 17

Well I know the answer is 1.0234.... So you would be correct!!! But what you're saying is all I had to do was 2^(1/03) and I would've gotten the right answer? That's all it is? THANK YOU ALL SO MUCH! <3

Answer 18

you mean 2^(1/30)

Answer 19

you can type
2^(1/30)=
into google to see the answer

Answer 20

Yes I do... And Thank you so much!!!