Question

Why are even and odd exponents significant when simplifying square root radical expressions?

Answer 1

\[\sqrt{x ^{6}} \sqrt{x ^{5}}\]

Answer 2

can't wait to see the answer to this

Answer 3

can you simplify both of those

Answer 4

Ok

Answer 5

No only 6

Answer 6

both can be simplified

Answer 7

what is x^6 simplified

Answer 8

Ummm 3

Answer 9

\[x ^{3}\]

Answer 10

now can you simplify x^5

Answer 11

No?

Answer 12

remember how jim said to simplify odd numbers?

Answer 13

\[\frac{ 5 }{ 2 }\]

Answer 14

\[2\frac{ 1 }{ 2 }\]

Answer 15

Ok. but how you get the 2 under it?

Answer 16

pair up the exponents to get them outside of the radical sign

Answer 17

\[\frac{ 6 }{ 2 }\]

Answer 18

\[x ^{3}\]

Answer 19

Ok.

Answer 20

\[x ^{2}\sqrt{x}\]

Answer 21

\[\sqrt{x^6}\]

does not simplify to \(x^3\)

Answer 22

\[\sqrt{x ^{6}}=\sqrt{x ^{2}}×\sqrt{x ^{3}}\]

Answer 23

0,o im confused....

Answer 24

two pairs of 3 when simplifying exponents in radicals they go outside the radical in x^2=x

Answer 25

So does x6 simplfy to 3?

Answer 26

yes

Answer 27

plug -1 into \(\sqrt{x^6}\) and \(x^3\)

what do you get?

Answer 28

I dont know 0,0 my teacher didnt show me that way... And where do you get -1

Answer 29

\[1=\sqrt{(-1)^6}\neq(-1)^3=-1\]

Answer 30

therefore \[\sqrt{x^6}\neq x^3\]

Answer 31

@Zarkon
\[x ^{3}\sqrt{-1}\] is the same thing as \[\sqrt{-1^{6}}\]

Answer 32

goes out as pairs of 2 in as multiples

Answer 33

:?

Answer 34

Holy hell im confused

Answer 35

\[\Large\sqrt{x^6}=|x^3|\]

Answer 36

@Zarkon sorry if im sounding rude right now but how would you simplify the radical x^6

Answer 37

i did...it is \[\large|x^3|\]

Answer 38

graph them on a calculator

Answer 39

Im like confused as hell 0,0. Like ifyou took a kid, and spun him on his head for ten minutes with out stopping, put him on his feet and made a dog chase him.. Thats me

Answer 40

XD

Answer 41

Im a dead serious right now... Im the kid running around like hes drunk while look back at the dog about to crap my pants

Answer 42

So if x6 isnt x3 then what is it?

Answer 43

It ends up being \(\Large\rm x^3\) sometimes,
and \(\Large\rm -x^3\) at other times.

\(\Large\rm |x|=\sqrt{x^2}=\pm x\)

When we apply an `even root` to an `even exponent`,
we have to write it like this.

Zarkon's example was good.
Lemme see if I can come up with another one :o hmm

Answer 44

So if it was a odd root, it would be the -x^3

Answer 45

Ahh the website froze on me :( grr

Answer 46

D:

Answer 47

Naw, odd roots don't give us trouble :d
They give us back the sign that we originally had.

Example:\[\Large\rm \sqrt[3]{-8}=-2\]We started with a negative, and ended up with a negative.
Good.

The negative that you put in front of x^3 is telling us we should have the opposite sign of whatever we start with. no no no :o\[\Large\rm \sqrt[3]{x^{12}}=x^4\]No negative to worry about when taking an odd root.

Answer 48

Oh oh I misread the question actually.
They were asking about `even/odd powers` not `even/odd roots`.
Hmm.

Answer 49

So with the 3sqrt x^12, youdivide the 12 by the 3?

Answer 50

Yes.
We can rewrite the expression like this:\[\Large\rm \sqrt[3]{x^{12}}=x^{12/3}\]

Answer 51

They specifically asked about `square` roots though.
Which is only the second root.

So this question is kinda strange...

Answer 52

Ok, so techincally, this question hs to have a answer like this:

If you had a odd power, your would have a answer in the exponent. But when you have a Even power, it will be one thing. for exaple. x^13 it would be \[x ^{5}\sqrt{x}\]

Answer 53

Well my spelling and grammar and word choice is poor tonight. im super tired

Answer 54

Hmm, yah I kinda like the way you're wording that.
You'll always be left with something under the root when you're applying it to the odd powered expression.

Odd power:
\[\Large\rm \sqrt{x^{13}}=\sqrt{x^{12}}\cdot\sqrt{x}=\pm x^6\sqrt{x}\]
Even power:\[\Large\rm \sqrt{x^{12}}=\pm x^6\]

Answer 55

Yes, thats what i meant, sorry i just havnt slept in like 2 days, been stressing out cuz im moving, but yes i meant it like that. just didnt know a way of wording it.

Answer 56

cool :)

Answer 57

:D so pretty much what i have to explain to my teacher, is write something like your example down, and explain why even and odds, which something like my answer would be

So the biggest part of why even and odd exponents are inportant are becuase with odd exponents you will be always left with something under the squareroot (More or less ouvariable) While even powers on the other hand, you will be left with nothing except the variable and the power

Answer 58

A Power*

Answer 59

Yehhhh, seems fine.
You could even maybe comment on how umm....

Even powers, when you take a square root will always give you an `integer` exponent in your result.
Example: \(\Large\rm \sqrt{x^6}=\pm x^3\)


Odd powers will always leave you with a `fractional` exponent.
Example: \(\Large\rm \sqrt{x^5}=x^{5/2}\)

Just another idea >.<
I'm not really sure what this is for, online assignment or something?
Hard to say exactly what they're looking for.
It's worded a little weird :)

Answer 60

Ya thats what i said, do u mind helping with 2 more. Not sureif they are right

Answer 61

Close this thread, it's getting too long.
Open your question in a new thread.
I'll stop by if I can c: Gotta do some stuff though.

Answer 62

ok thamks