Question

Simplify 5 root(4)(256x^3) completely. Write answer in radical form. Assume x>0.

Answer 1

\[\Large 5\sqrt[4]{256x^3}?\]

Answer 2

hint:
\[\sqrt[4]{256x^3} \implies \sqrt[4]{4 \times 4 \times 4 \times 4 \times x^3}\]
does that help?

Answer 3

@lgbasallote So thats what its wanting me to do?

Answer 4

depends on how you interpreted what i said..

Answer 5

so would it be 16xroot(4)(x)

Answer 6

@lgbasallote

Answer 7

nope..

Answer 8

\[\sqrt[4]{4 \times 4 \times 4 \times 4 \times x^3} \implies \sqrt[4]{4^4 \times x^3} \implies \sqrt[4]{4^4} \times \sqrt[4]{x^3}\]

Answer 9

Oh I sort it... so its 256/4

Answer 10

is that giving you an idea now?

Answer 11

Yeah so is it 4xroot(4)(x)

Answer 12

@lgbasallote

Answer 13

Am I right now?

Answer 14

still no

Answer 15

\[\Large \sqrt[4]{x^3} \ne x\sqrt[4]{x}\]

Answer 16

\[\sqrt[4]{x^5} = x\sqrt[4]{x}\]

Answer 17

OMG! This is so frustrating I feel dumb :(

Answer 18

you cant take x^3 out of the 4th root

Answer 19

I still don't get but you can take 2 and leave one x inside right? what happenes to the 256 I still don't get it? Thats not divided by four

Answer 20

@lgbasallote

Answer 21

it's not divided by 4

Answer 22

if it's \(\sqrt x^3\) then you're right it's \(x\sqrt x\)
however it's 4th root

Answer 23

so you cant do it

Answer 24

\[\sqrt x^3 = x^{3/2} \]
\[\sqrt[4]{x^3} = x^{3/4}\]
do you see the difference?

Answer 25

i dont get where you're getting confused...will you tell me where?

Answer 26

i think you're too accustomed to square root that you're looking at this like square root. this is 4th root

Answer 27

So then it cant be done?

Answer 28

@lgbasallote

Answer 29

perhaps a demonstration

\[\large \sqrt[4]{16 x^2} \implies \sqrt[4]{2 \times 2 \times 2 \times 2 \times x^2} \implies \sqrt[4]{2^4 x^2} \implies 2\sqrt[4]{x^2} \implies 2\sqrt x\]

Answer 30

here's another one
\[\large \sqrt[4]{81x^3} \implies \sqrt[4]{3 \times 3 \times 3 \times 3 \times 3 \times x^3} \implies \sqrt[4]{3^4 x^3} \implies 3\sqrt[4]{x^3}\]

Answer 31

so then its root(4)(4^4x^3) 4root(4)(x^3) ? @lgbasallote

Answer 32

another one
\[\large\sqrt[4]{256x^5} \implies \sqrt[4]{4 \times 4 \times 4 \times 4 \times x^5} \implies \sqrt[4]{4^4 x^5} \implies 4x\sqrt[4]{x}\]

Answer 33

yes!!!

Answer 34

but wiat..that's just \[\sqrt[4]{256x^3}\]
remember the question is \[\large 5\sqrt[4]{256x^3}\]

Answer 35

so then you do \[5 \times 4 \sqrt[4]{x^3}\]

Answer 36

\[20\root(4)\sqrt{x^3}\]

Answer 37

20root(4)(X^3)

Answer 38

right

Answer 39

WOOOOO THANKS SO MUCHHHHH!!!! :D YOU ARE THE BEST!!! @lgbasallote

Answer 40

haha you're welcome ^_^

Answer 41

@lgbasallote So how would I do -5root(5)(32x^13)

Answer 42

32 = 2^5

Answer 43

\[\large\sqrt[5]{32x^{13}} \implies \sqrt[5]{2^5 x^{13}}\]

Answer 44

\[\implies \sqrt[5]{2^5 \times x^{10} \times x^3}\]

Answer 45

do you see it now?

Answer 46

2x^2root(5)(x^3) ? @lgbasallote

Answer 47

yes!!!

Answer 48

WOOOOOO!!! Now I get it more it's just confusing the sqrt gets me every time @lg

Answer 49

i need to go now so i hope you get these :DDD

Answer 50

haha i know..it just takes practice and experience

Answer 51

Thanks so m,ouch again! God Bless!!!! @lgbasallote