Question

simplifying radicals.

Answer 1

@DanJS

Answer 2

ok

Answer 3

Here is the question:
-\[\sqrt[4]{96x ^{8}y ^{4}}\]

Answer 4

k, write out each step

Answer 5

sorry, there is a negative before the equation

Answer 6

Okay firstly, you times 8*1/8

Answer 7

and 4*1/4

Answer 8

right?

Answer 9

this one is a bit easier than the last

Answer 10

so it's:
\[-\sqrt[4]{96xy}\]

Answer 11

\[(-1) * \sqrt[4]{96 * x^8*y^4}\]

first take down the radical on teh x and y and make them to the 1/4th power

Answer 12

Okay so it's 1/8*4 and 4*1/4

Answer 13

\[(-1) * \sqrt[4]{96 * x^8*y^4} = (-1) *\sqrt[4]{96}*[x^8]^{1/4} * [y^4]^{1/4}\]

Answer 14

[x^8]^(1/4) = x^(8/4) = x^2

Answer 15

(y^4)^(1/4) = y^(4/4) = y

Answer 16

OH! I get it!

Answer 17

: )

Answer 18

so now it looks like:
\[-1\sqrt[4]{96x ^{2}y}\]

Answer 19

except you move 'em over...the x^2 and y

Answer 20

right, they are outside the root now

Answer 21

okay so, before I move 'em over I'll find the perfect square of 96

Answer 22

\[-1*\sqrt[4]{96}*x^2*y\]

Answer 23

for the 4th root of 96, start breaking down 92 into smaller factors

96 = 2*48 = 2*2*24 = 2*2*2*12 = 2*2*2*2*6

Answer 24

there you see you have 4 2's

96 = 2^4 * 6

Answer 25

So to find the perfect square of 96 this is what I did:

96/2
48/4
12/6
=2

Answer 26

It is the 4th root, not square.

I just kept dividing by 2, and pulling 2's out of 96

96 = 2 * 2 * 2 * 2 * 6

Answer 27

\[\sqrt[4]{96} = \sqrt[4]{2^4*6} = 2*\sqrt[4]{6}\]

Answer 28

[2^4]^(1/4) = 2^(4/4) = 2

Answer 29

oh! just keep dividing by two's! So throughout these problems you are continually using that 4 on the root?

Answer 30

right, the 4th root of (96*x^8*y^4) is the same as (96*x^8*y^4)^(1/4)

Answer 31

That makes so much more sense! I had no idea what that was for!

Answer 32

right, so what is the final answer

Answer 33

So final answer:
\[-2x ^{2}y \sqrt[4]{6}\]

Answer 34

in my math class they put the x and y variables on the other side.

Answer 35

in front of the root ?

Answer 36

yup! I don't know...it's weird that way but that's what they say is right.

Answer 37

It really doesn't matter, but usually the numbers are in front of the variables

Answer 38

If you want to do another, i have time for one more

Answer 39

YOU HAVE BEEN SO EPICLY AMAZING! I do have one more that I would like to do because it does have a number by the square root like this problem had the number 4.

Answer 40

*it doesn't

Answer 41

should I open it in a new question and then tag you and close it?

Answer 42

yeah

Answer 43

k