Question

Simplify each of the following expressions using i in the final answer.

Answer 1

\[\sqrt[10]{-81/25}\]

Answer 2

\[\sqrt[10]{\frac{-81}{25}}\] is not a real number
are you sure about the minus sign?

Answer 3

Yes, that's why it says use i.

Answer 4

ok we can start with
\[\sqrt[10]{\frac{9^2\times( -1)}{5^2}}\]

Answer 5

\[\sqrt[10]{-2025/25}\]

Answer 6

did you just change the question?

Answer 7

\[\frac{-2025}{25}=-81\] so you have
\[\sqrt[10]{-81}\]

Answer 8

this is the same as
\[\sqrt[10]{9^2\times (-1)}\]
which is equal to
\[\sqrt[5]{9}\sqrt[10]{-1}\]

Answer 9

Yep

Answer 10

and now you have a ton of work to do, because \(-1\) has ten tenth roots!

Answer 11

is this a class in complex variables?

Answer 12

No, real numbers

Answer 13

then you don't know how to do this
\(-1\) has, as i said, ten tenth roots

Answer 14

you sure it is the tenth root, right? not the square root?

Answer 15

Positive

Answer 16

\(\large \sqrt[10]{\frac{9^2\times( -1)}{5^2}}\)

\(\large \sqrt[10]{\frac{9^2\times i ^2}{5^2}}\)

\(\large \sqrt[10]{(\frac{9 i }{5})^2}\)

\(\large \sqrt[5]{\frac{9 i }{5}}\)

Answer 17

may be lev it like that

Answer 18

AAAAAAAAAAAAAAAAAAAAAAAAAHHHHHHHHHHHHHHHHHHHHHHHH

Answer 19

ahhh my foot
you cannot have a complex number in standard form with an \(i\) inside a radical

Answer 20

not that @ganeshie8 is incorrect, but that is no way to write a complex number

Answer 21

Oe sec

Answer 22

another one for my "bad math" pile
second in the last 5 minutes

Answer 23

some info we loose when we simplify like that @satellite73 ? :)

Answer 24

i mean, do we loose some info... when we write -1 = i^2 and simplify the radical ?

Answer 25

wolfram also not simplifying -1 inside radical

Answer 26

http://www.wolframalpha.com/input/?i=%28-81%2F25%29%5E%281%2F10%29

Answer 27

there is a standard form of a complex number
it is \(a+bi\)
if you don't want to write the number in standard form, why change it at all? for example, why not leave \(\frac{2+3i}{1-i}\) as it is? a fraction with one complex number over another?

Answer 28

the problem also: what exactly does \(\sqrt[5]{i}\) mean?

Answer 29

as you see, wolfram just says \(\sqrt[10]{-1}=\sqrt[10]{-1}\) just leave it like that?

Answer 30

beautiful! when i get to 200, i am publishing my book
this question was written by a person who should not teach math or write math questions

Answer 31

lol i think 10 is floating outside stand alsone

Answer 32

ooooh !! perhaps that ten is a coefficient!!!!

Answer 33

^^

Answer 34

now it makes sense and i take it all back!

Answer 35

\[\sqrt{\frac{-81}{25}}=\frac{9}{5}i\] that makes sense!

Answer 36

OOOHHH

Answer 37

How bout the other one?

Answer 38

other one also,
treat 20 and 12 as just coefficients

Answer 39

Never mind, THANK YOU SO MUCH!!! :)

Answer 40

\(\large \sqrt{\frac{-1}{100}}=\frac{1}{10}i \)