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# Did i rationalize this correctly?

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1. http://prntscr.com/awxuxy

Is this correct?

Or was the demoninator ment to be 3? because root 2 multiply by root 2 gives root 4 and the root of 4 is = 2 so then do you do 2 + 1 ? or 2 x 1?
2. No. so far as I can tell you have multiplied up and down by root 2. In this case you multiply up and down by the conjugate of the bottom. (i.e. swap the sign on the root bit to give 1 - root 2).

This works because it all depends on the difference between two squares which causes the root bit to disappear from the denominator when multiplied out hence

Which I would leave in that form although if the Q asked for it to be fully expanded would become

3. (Original post by nerak99)
No. so far as I can tell you have multiplied up and down by root 2. In this case you multiply up and down by the conjugate of the bottom. (i.e. swap the sign on the root bit to give 1 - root 2).

This works because it all depends on the difference between two squares which causes the root bit to disappear from the denominator when multiplied out hence

Which I would leave in that form although if the Q asked for it to be fully expanded would become

I thought when your rationalize you have to multiply by the denominator.. Im a bit confused now, because I just watched a video where is shows you how to rationalize the denominator and it says you multiply the root at the bottom (denominator) at both top and bottom. ugh
4. That only applies where the denominator is only a root and not of the form .

Hence: rationalise
5. (Original post by nerak99)
That only applies where the denominator is only a root and not of the form .

Hence: rationalise
So what do you do when it is that form? Sorry im just confused
6. (Original post by junayd1998)
So what do you do when it is that form? Sorry im just confused
You have two forms:

1. - in this case, you multiply top and bottom by .

2. - in this case, you multiply top and bottom by (i.e: you flip the sign next to the square root, if it's a + it becomes -, if it's a - it becomes a +).
7. (Original post by junayd1998)
So what do you do when it is that form? Sorry im just confused
By "that" I assume you mean in the numerator and in the denominator and in that case you can just multiply top and bottom by .

Example

If the form is

the x in the numerator is any bit of algebra you like
8. (Original post by Zacken)
You have two forms:

1. - in this case, you multiply top and bottom by .

2. - in this case, you multiply top and bottom by (i.e: you flip the sign next to the square root, if it's a + it becomes -, if it's a - it becomes a +).
Ah i understand never knew the second form, I was only aware of the first one. Thanks i get it now
9. (Original post by Zacken)
You have two forms:

1. - in this case, you multiply top and bottom by .

2. - in this case, you multiply top and bottom by (i.e: you flip the sign next to the square root, if it's a + it becomes -, if it's a - it becomes a +).
http://prntscr.com/ax56l2

Have I done this correctly? I'm a bit unsure.
10. (Original post by junayd1998)
http://prntscr.com/ax56l2

Have I done this correctly? I'm a bit unsure.
Perfect, now simplify the 1-2.
11. (Original post by Zacken)
Perfect, now simplify the 1-2.

http://prntscr.com/ax5bng

That any good?
12. (Original post by junayd1998)
http://prntscr.com/ax5bng

That any good?
Nooo, 5 - sqrt(2) is not 5sqrt(2). Instead (5 - sqrt(2)) / -1 = sqrt(2) - 5
13. (Original post by Zacken)
Nooo, 5 - sqrt(2) is not 5sqrt(2). Instead (5 - sqrt(2)) / -1 = sqrt(2) - 5
http://prntscr.com/ax607w

So that? The other way round?
14. (Original post by junayd1998)
http://prntscr.com/ax607w

So that? The other way round?
Perfect.
15. (Original post by Zacken)
Perfect.
Can i ask why we do it that way round? Because with a question like this http://prntscr.com/ax63xb the number comes first then the root with the number. Sorry for the annoyance just want to make sure I know it all correctly
16. (Original post by junayd1998)
Can i ask why we do it that way round? Because with a question like this http://prntscr.com/ax63xb the number comes first then the root with the number. Sorry for the annoyance just want to make sure I know it all correctly
There is a massive difference between which is the number multiplied by the number and which is the number added to the number .

If you want, you could have written (they mean the same thing) but they are very different from or .

It's like you saying that is the same thing as .
17. (Original post by Zacken)
There is a massive difference between which is the number multiplied by the number and which is the number added to the number .

If you want, you could have written (they mean the same thing) but they are very different from or .

It's like you saying that is the same thing as .
Oh okay I understand Thanks
18. (Original post by junayd1998)
Oh okay I understand Thanks
Awesome.
19. The correct answer is, -5 +5√2
20. (Original post by junayd1998)
Oh okay I understand Thanks
As above - (I have no clue how this slipped my eye) but the correct answer should be , i.e: you need to multiply out the as and not as .

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