Question

how do i solve the cubed root of 3xcubed ytothe 5?

Answer 1

you can write that as cuberoot(xxxyyyyy); then take out the triples

Answer 2

what about the cubed root of 24x^15 y^6?

Answer 3

so take out 3 of the x and 3 of the y and that leaves two y, so
\[xy \sqrt[3]{y^2}\]

Answer 4

ok i had an answer similar to that, but not that exact one.

Answer 5

take out as many triples as you can; and factor 24 into prime factors

Answer 6

im not understanding the triples thing.

Answer 7

24 is 2x2x2x3

Answer 8

exactly... there are 3 2s so they can come out

Answer 9

cuberoot(24) is 2 times cuberoot(3)

Answer 10

fifteen xs so you can pull 5 triples out (all of them)

Answer 11

so its 2x^5

Answer 12

on the outside?

Answer 13

or is the answer 2x^5 y^2?

Answer 14

so far, but dont forget the ys

Answer 15

yes... but there is something left under the radical

Answer 16

3?

Answer 17

yes

Answer 18

you got it.... for square roots you pull out pairs, for cube roots you pull out the triples

Answer 19

so the answer is 2x^5 y^2 cube root 3?

Answer 20

I really appreciate your help. There is one more I need help with. It is under a square root, but is a fraction

Answer 21

but be careful... this is the way to do single terms like these, but
\[\sqrt{x^6 + y^2}\] is not x^3+y

Answer 22

yes, that is the answer... dnag you are good

and let's see the fraction

Answer 23

thank you!

Answer 24

I'm not sure how to write it, but its cube root of 72x^15 y^13/64x^12 y^9

Answer 25

\[\sqrt[3]{72x^15y^13 \over 64x^12y^9}\]

Answer 26

simplify it first ... write the numbers as prime factors and cancel as much as you can

Answer 27

i need some help with that. I don't understand.

Answer 28

you can cancel 12 xs and 9 ys right off the bat

Answer 29

so is it cube root of 72x^3 y^4/64xy?

Answer 30

\[{x^{15} \over x^{12} } = x^3\]

Answer 31

15 - 12 leaves 3 xs, and they happened to be on top

Answer 32

so there are none left on the bottom, just the 64?

Answer 33

exactly... got lucky this time

Answer 34

with the problem I mean, you are doing great

Answer 35

thank you.

Answer 36

so then i factor 72 and 64 or?

Answer 37

now cancel out the common factors in 72 and 64

Answer 38

yes, thats how to do it

Answer 39

3x3x2x2x2?

Answer 40

thats 72 it seems

Answer 41

3x3x2x2x2 / 2x2x2x2x2x2
3x3 - - - - - - 2x2x2

Answer 42

2x2x3x3?

Answer 43

i know that last one is wrong.

Answer 44

keep dividing by 2 until you can't do it any more
then see if what is left is prime

Answer 45

idk

Answer 46

64 is 2x2x2x2x2x2

Answer 47

right so that is 3

Answer 48

because there are 3 sets right?

Answer 49

not yet, we are trying to simplify... cancelling what we can

Answer 50

oh

Answer 51

that 72 is still up there, I mean the 3x3x2x2x2

Answer 52

so 3x3x2x2x2 / 2x2x2x2x2x2 is
3x3 - - - - - - 2x2x2

Answer 53

cacelled out 2x2x2 from top and bottom

Answer 54

ok

Answer 55

so that leaves 9 x^3y^4 over 8 in the radical

Answer 56

what goes on the outside?

Answer 57

we havent pulled anything out yet, just simplified it
you pick the triples to pull out (since this is a cube root)

Answer 58

is it just one y on the outside?

Answer 59

\[\sqrt[3]{9x^3y^4 \over 8}\]

Answer 60

yes, pull 3ys out, one ouside and leaves one inside

Answer 61

\[3y^{3}\] and \[x^{3}\] on the outside

Answer 62

and then 9y/8 on the inside?

Answer 63

almost... but when you take 3 of something from inside, it is 1 on the outside
so an x and a y and the 1/8 can come out

Answer 64

which does leave 9y inside ... and the cube root of 1/8 is 1/2

Answer 65

1/8xy on the outside

Answer 66

1/2 x y on the outside

Answer 67

x is the cube root of x cubed .... y is the cube root of y cubed ....
1/2 is the cube root of 1/8

Answer 68

so an x outside represents 3 inside, and so on

Answer 69

ok so then its just x^2 y^2 on the inside?

Answer 70

just a y on the inside?

Answer 71

I think the answer is:
\[{1 \over 2}xy \sqrt[3]{9y}\]

Answer 72

you are right.

Answer 73

you can check it by cubing what is on the left and multiplying that by what is under the radical

Answer 74

there are lots of shortcuts, but they always confuse me
I like doing things the long simple way

Answer 75

okay great. thank you so much for your help. that was a hard one.

Answer 76

only because of the typing... you knwo what you are doing
keep up the good work

Answer 77

thank you.