Question

@mathmale How do I write this in simplest form?
Square root 2 - square root 6 / square root 2 + square root 6

Answer 1

\[\sqrt{2} - \sqrt{6} / \sqrt{2} + \sqrt{6} \]

Answer 2

I'd be very interested in seeing what you've done already.

Answer 3

Great minds think alike, don't they? :)

Answer 4

All I did was take out the individual square roots and swap them for a big one over the whole thing.

Answer 5

Excuse my pickiness, but you do have to enclose the first 2 and the last 2 terms inside parentheses. See why?

Answer 6

I don't see why

Answer 7

This\[\frac{ \sqrt{2}-\sqrt{6} }{ \sqrt{2}+\sqrt{6} }\] is my interpretation of the original problem:

Answer 8

Is it your interpretation also?

Answer 9

Yes(:

Answer 10

Forgive my temporary absence. My point is that if you don't enclose the first 2 terms and then the last 2 terms in ( ), some readers may not grasp that we intended for the first 2 terms to constitute one quantity and the last 2 terms another quantitiy.

Answer 11

Oh, I see what you mean.

Answer 12

In this particular problem, Nicole, you want to eliminate the radicals fromthe denominator. That's what "simplest form" means here.

The conjugate of Sqrt(2) + Sqrt(6) is Sqrt( 2) - Sqrt (6). Multiply top and bottom of your fraction by that. You'll end up with an interger quantity in the denom, which is what we wanted.

Answer 13

Lo and behold, no more radicals will exist in the denom.

Answer 14

Okay, one moment

Answer 15

Will you still have the roots in top? Or do I times both top and bottom?

Answer 16

Yes, you'll still have some radicals in the numerator, which is fine. Radicals in the denom. are not so fine. ;)

Answer 17

Okay ha

Answer 18

I never crack jokes, you know. ;)

Answer 19

Never? :P
So because it Sqrt(2) + Sqrt(6) times Sqrt( 2) - Sqrt (6) it will coming out to be 2 - 6 on bottom?

Answer 20

Exactly, which reduces to what negative number?

Answer 21

-4

Answer 22

Oh, really? Yes, of course, you're right.

Answer 23

So after you get -4 on the bottom, you have to simplify the top. do I take it out the roots?

Answer 24

No. combine similar terms as far as possible, and then leave the resulting fraction as is.
Or, get rid of that (-) sign in the denom and put it in the num. instead.

Answer 25

Can you show the steps, if any, after w get -4?

Answer 26

*we

Answer 27

Yeah, we. We make a good team.
You already have a numerator, I assume. Simply enclose it in parentheses and stick a (-) sign in front of it, rewriting the den. as simply 4.
You could leave your result like that, or you could distribute that (-) sign over to everything within your set of parenthteses.

Answer 28

Haha:P
I unfortunately don't have that as an answer choice:/ Unless i'm reading it wrong and the image of what it looks like isn't clicking in my head..

Answer 29

Maybe I did something wrong? @mathmale

Answer 30

I haven't actually done the problem myself, Nicole, since we were certainly on the right track. Is it possible for you to share an image of what you've written?

Answer 31

Yes, one second.

Answer 32

Seeing this image is SO helpful. Nicole, you need to multiply BOTH numerator and denom. of your fraction by Sqrt(2)-Sqrt(6). Mind trying again?

Answer 33

oh, ha yes i redo it :P

Answer 34

*I'll

Answer 35

\[\sqrt{4} + \sqrt{36} \] For the top?

Answer 36

I need just a sec.

Answer 37

Okay

Answer 38

Yes, yoiu're doing fine. But remember that Sqrt(4)=2 and Sqrt(36)=6. So your final answer becomes >>> ?

Answer 39

8 over -4?

Answer 40

Looks good! And 8 over -4 reduces to what? :)

Answer 41

4 over -2 which goes to -2?

Answer 42

Nice going, Nicole! I'm getting dizzy after having concentrated on OpenStudy questions for the past three hours or so, so forgive me if I leave soon. Looking forward to meeting you again online. All the best. MM

Answer 43

Thank you for your help but I think we or I did something wrong, I don't have a simple -2 as an answer choice :( @mathmale

Answer 44

Give me a mom. and I'll go thru the problem myself.

Answer 45

Okay, these are my choice, maybe it will help:/

Answer 46

*Choices

Answer 47

Found the problem. We need to multiply as follows:\[(\sqrt{2}-\sqrt{6})(\sqrt{2}-\sqrt{6})\]

Answer 48

\[\sqrt{4} - \sqrt{12} - \sqrt{12} - \sqrt{4} ?\]

Answer 49

Oh, \[\sqrt{36}\]

Answer 50

On the end not - 4 ha