Question

radical expression

Answer 1

@DanJS

Answer 2

k

Answer 3

Here is the question:
\[\sqrt{80x^3y^6z^2}\]

Answer 4

but this time it doesn't have another number there...what now?

Answer 5

That is the square root, everything under it is to the 1/2 power

Answer 6

so I would think of it the same as this:
\[\sqrt[2]{80x^3y^6z^2}\]

Answer 7

yep

Answer 8

great!

Answer 9

First step:

Answer 10

1/2*3 = 3/2
1/2*6 = 3
1/2*2 = 1

Answer 11

yep, that is what happens to the powers

Answer 12

Just think, whatever the root is, divide all the powers by that number

Answer 13

so the x is x^3/2 isn't not supposed to be a fraction or decimal? how do you make it a whole number?

Answer 14

*isn't it

Answer 15

\[\sqrt[]{80x^3y^6z^2} = \sqrt{80 *x *x^2 *y^6*z^2} = \sqrt{80x}*x*y^2*z\]

Answer 16

you could leave it as x^(3/2) or from that other prob we did, they like to leave part of it under the root , like that above

Answer 17

oh! I get it!

Answer 18

now for the perfect square of 80

Answer 19

is 10 or 20 a perfect square?

Answer 20

there isn't one, but you can decompose 80 into factors that may contain a perfect square

Answer 21

80 = 2 * 40 = 2 * 2 * 20 = 2 * 2 * 2 * 10 = 2 * 2 * 2 * 2 * 5

so

80 = 2^4 * 5

Answer 22

is 5 a perfect square??

Answer 23

I decomposed it to a 5 on my calculator but I didn't think 5 was a perfect square.

Answer 24

no, 5 is the term that stays under the root
\[\sqrt{80} = \sqrt{2^4 * 5} = \sqrt{2^4}\sqrt{5} = 2^2\sqrt{5} = 4\sqrt{5}\]

Answer 25

So it is the 2^4 that needs to be a perfect square??

Answer 26

yeah
2^4 is the same as (2^2)^2 = 4^2

Answer 27

okay. so the answer would look like this:
\[4xy^3z \sqrt{5x}\]

Answer 28

you just break the 80 down into factors, and see if you can find any factors that appear 2 times, you can take those out of the root,
\[\sqrt{80} = \sqrt{4*4 * 5} = \sqrt{4^2*5} = \sqrt{4^2}\sqrt{5} = 4^{2/2}\sqrt{5} = 4\sqrt{5}\]

Answer 29

\[\sqrt{80x^3y^6z^2} = 4 xy^2z \sqrt{5x}\]

Answer 30

Yes, I see it. I just wanted to thank you so much because I have my final math exam on Tuesday and I have not for the life of me been able to understand radicals! Going on openstudy was the end of the line after I had gone through my lesson material 10+ times. You are truly amazing! I have not gotten as good of help from some others on openstudy. I will continue doing problems like the way you taught me! My lesson taught me differently---SO CONFUSING! You are the BEST!!!!!! :D

Answer 31

awesome, glad you understand :)

Answer 32

THANKS AGAIN!

Answer 33

welcome, i am usually on here once a day at least, feel free to tag me or whatever if you have more to do

Answer 34

it only took 3 examples, you got it down now

Answer 35

YES! hopefully I remember everything!