Question

Simplify, help please??!! This one's harder...

Answer 1

\[\LARGE 5\sqrt[3]{96}\]

Answer 2

@hartnn

Answer 3

Thanks, @Algebraic! He went offline because of you!!! He actually helped me & explained it! I am VERY upset with you -____-

Answer 4

it's all very sad.

Answer 5

you need to factor 96 and see if it contains any perfect cubes

Answer 6

;_; b

Answer 7

but thumbs up anyway.

Answer 8

@satellite73 I don't know how to do that... Will you please explain?

Answer 9

how to factor? sure

Answer 10

Btw, answer choices (sorry forgot):
\[\large A) 20\sqrt[3]{6}\]
\[\large B) 10\sqrt[3]{12}\]
\[\large C) 7\sqrt[3]{12}\]
\[\large D) 2\sqrt[3]{12}\]

Answer 11

but before we do that, lets see what the answer is,
there are not too many perfect cubes to check
\(2^3=8\) and \(3^3=27\) so lets check for 8
if your multiplication tables are very good then you may recognize \(96=8\times 12\) so
\[\sqrt[3]{96}=\sqrt[3]{8}\sqrt[3]{12}=2\sqrt[3]{12}\]

Answer 12

meaning your "final answer" will be
\[5\times 2\sqrt[3]{12}=10\sqrt[3]{12}\]

Answer 13

Wait, you confused me on that last part. Can you elaborate a little more, please?

Answer 14

idea is you are looking to see if 96 contains any perfect cubes
do you know what i mean by "perfect cube"?

Answer 15

Yes

Answer 16

perfect cubes means the cube of some whole number
let me list some
\(2^3=8,3^3=27,4^3=64,5^3=125\) and so on

Answer 17

so now i am looking at \(\sqrt[3]{96}\) ignoring the 5 out front, because it is not important in this computation
i want to know if there are any perfect cubes that are factors of 96 so i start with 8 (because it is the smallest)

Answer 18

i see that 8 goes in to 96 evenly, because \(96=8\times 12\)

Answer 19

and i know that the cube root of 8 is 2 (because i know \(2^3=8\) so i pull a 2 outside of the radical, and leave the 12 inside

Answer 20

Yes.

Answer 21

that tells me that
\[\sqrt[3]{96}=2\sqrt[3]{12}\]

Answer 22

now i remember that i started with
\[5\sqrt[3]{96}\] so i end up with
\[5\times 2\sqrt[3]{12}=10\sqrt[3]{12}\]

Answer 23

Oh, okay! I think I understand now :) Thank you so much for taking the time to explain it to me. Sometimes it just doesn't process :)