Question

Help me simplify this radical expression.

Answer 1

\[\frac{ 24\sqrt[3]{1296} }{ 4\sqrt[3]{54} }\]

Answer 2

After factoring out all the cube roots I ended up with

\[\frac{ 144\sqrt[3]{5} }{ 12\sqrt[3]{2} }\]

Answer 3

Now im not sure this will equal to any of my answer choices

Answer 4

@Nnesha

Answer 5

no help me lol

Answer 6

probably another simple thing i can't see to give me my final answer

Answer 7

With square roots, if you multiply two square roots with the same radicand together, you'll eliminate the square root

ex

\[\Large \sqrt{5}*\sqrt{5} = 5\]

we multiply two copies of sqrt(5)

Answer 8

i see, so i should do that here?

Answer 9

for cube roots, you need 3 copies

ex

\[\Large \sqrt[3]{9}*\sqrt[3]{9}*\sqrt[3]{9} = 9\]

Answer 10

so if you had a normal square root in the denominator, you would multiply top and bottom by the radical in the denominator (so you'll end up with 2 copies of the roots multiplying)

Answer 11

In this case, we have a cube root in the denominator

so you need to tack on two additional copies of \(\Large \sqrt[3]{54}\). Then you'll have 3 copies of \(\Large \sqrt[3]{54}\) multiplied

Answer 12

So we have to multiply top and bottom by \(\Large \sqrt[3]{54}*\sqrt[3]{54}\)

to go from

\[\Large \frac{ 24\sqrt[3]{1296} }{ 4\sqrt[3]{54} }\]

to get to

\[\Large \frac{ 24\sqrt[3]{1296} {\color{red}{*\sqrt[3]{54}*\sqrt[3]{54}}} }{ 4\sqrt[3]{54}{\color{red}{*\sqrt[3]{54}*\sqrt[3]{54}}} }\]

Answer 13

i'll try that, but what do I do from the point where i factored the cubes? ^^

Answer 14

what do you mean

Answer 15

the 2nd post on this thread i attempted to simplify the cube roots

Answer 16

do you see it?

Answer 17

yeah, you made an error though when simplifying

Answer 18

which one?

Answer 19

the radicand in the numerator

Answer 20

i don't see my error

Answer 21

tell me what it is?

Answer 22

1296 = 216*6 = 6^3*6

so,

\[\Large 24\sqrt[3]{1296} = 24\sqrt[3]{6^3*6}\]

\[\Large 24\sqrt[3]{1296} = 24\sqrt[3]{6^3}*\sqrt[3]{6}\]

\[\Large 24\sqrt[3]{1296} = 24*6*\sqrt[3]{6}\]

\[\Large 24\sqrt[3]{1296} = 144\sqrt[3]{6}\]

Answer 23

you had 5 under the root, when it should be 6

Answer 24

Oh i see it now. but what do i do after this?

Answer 25

You would apply the rule I used before I simplified \(\Large 24\sqrt[3]{1296} = 144\sqrt[3]{6}\)

Answer 26

multiply by radical 2 twice?

Answer 27

basically 3 times?

Answer 28

You have

\[\Large \frac{ 144\sqrt[3]{6} }{ 12\sqrt[3]{2} }\]

multiply top and bottom by two copies of \(\Large \sqrt[3]{2}\) to rationalize the denominator.

Answer 29

yes correct, so you'll have 3 copies of that cube root which multiply to a rational number

Answer 30

What are the rules for the cube root when multiplied, does that change?

Answer 31

which rules are you thinking of

Answer 32

\[144\sqrt[3]{6}\times \sqrt[3]{2}\times \sqrt[3]{2}=144\sqrt[3]{24}?\]

Answer 33

good, then you can simplify that radical (since one factor of 24 is a perfect cube)

Answer 34

so the denominator just becomes 24?

Answer 35

yes

Answer 36

once all the radicals are simplified, you can reduce the fraction

Answer 37

ooh got it from here. thanks dude.

Answer 38

no problem