Question

radical question

Answer 1

@DanJS

Answer 2

brb 1 min

Answer 3

\[\sqrt[3]{\frac{ 16 }{ 125 }?}\]

Answer 4

okay. sorry i didn't know how to get rid of the question mark.

Answer 5

I'll just start typing through the process. So, with this problem I know that you separate the fraction like this:
\[\frac{ \sqrt[3]{16} }{ \sqrt[3]{125} }\]
right?

Answer 6

ok, yep you can do that

Answer 7

16 = 2 * 2 * 2 * 2
and
125 = 5 * 5 * 5

Answer 8

Okay so the top will be
\[3\sqrt{2*6}\]

Answer 9

oh nevermind. that won't work

Answer 10

\[\sqrt[2]{8*2}\]

Answer 11

*3

Answer 12

the bottom is easy

\[\sqrt[3]{125} = 125^{1/3} = (5*5*5)^{1/3} = [5^3]^{1/3} = 5^{3/3} = 5^{1}=5\]

Answer 13

Recall the nth root of something is the same as that something to the 1/nth power
\[\sqrt[n]{x} = x ^{1/n}\]

Answer 14

yes, i remember.

Answer 15

k, so the cubed root of 125 is 5

Answer 16

I get that. I was able to input the bottom fraction on my calculator and it came up 5.

Answer 17

right, 125 = 5*5*5 , cubed root of 125 = 5

Answer 18

for the top
\[\sqrt[3]{16} = \sqrt[3]{2*2*2*2} = \sqrt[3]{2^3 * 2}\]

Answer 19

overall you get 2 times the cubed root of 2
\[\sqrt[3]{16} = 2*\sqrt[3]{2}\]

Answer 20

\[\sqrt[2]{2^{3}*2}\]
is the same thing as
\[\sqrt[3]{8*2}\]

Answer 21

yeah, and 8*2 is 16, the original number

Answer 22

the way i usually try to simplify radicals, is break the number down into its prime factorization first.

16 = 2*2*2*2

Answer 23

Okay. So final answer:
\[\frac{ 2\sqrt[3]{2} }{ 5 }\]

Answer 24

cubed root means you can take out any factor that appears 3 times

Answer 25

Okay. I will write it out next time so I don't get confused.

Answer 26

16 = 2^3 * 2

Answer 27

yeah that is the final answer

Answer 28

Thanks! one more? and then I gotta go.

Answer 29

sure