PerplexedBird
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5- root3 / 2 + root3

in form of a + b root3 where a and b are integers
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Chlorophile
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(Original post by PerplexedBird)
5- root3 / 2 + root3

in form of a + b root3 where a and b are integers
What've you done so far?
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PerplexedBird
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(Original post by Chlorophile)
What've you done so far?

Nothing I'm perplexed...
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Chlorophile
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(Original post by PerplexedBird)
Nothing I'm perplexed...
We want to get rid of the surd at the bottom. What do you think we could multiply 2+root3 by to get rid of the surd?
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Abbie :)
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(Original post by PerplexedBird)
Nothing I'm perplexed...
To make it easier and the answer more obvious, separate them into two separate fractions, then go by rules of how to divide two fractions.
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Chlorophile
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(Original post by Abbie :))
To make it easier and the answer more obvious, separate them into two separate fractions, then go by rules of how to divide two fractions.
I don't think that is what you should do... This is a rationalising denominators question. All you need to do is multiple the top and bottom by a specific number, which the OP should hopefully be able to work out.
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Abbie :)
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(Original post by Chlorophile)
I don't think that is what you should do... This is a rationalising denominators question. All you need to do is multiple the top and bottom by a specific number, which the OP should hopefully be able to work out.
I'd usually do it by rationalising the denominator, this is just a way a friend who was better at maths than myself showed me when I was struggling to understand how to do that.

edit; looking over it I don't even know if his method is mathematically sound :mad:.
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PILEDRIV3R WALTZ
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(Original post by Chlorophile)
I don't think that is what you should do... This is a rationalising denominators question. All you need to do is multiple the top and bottom by a specific number, which the OP should hopefully be able to work out.

(Original post by PerplexedBird)
5- root3 / 2 + root3

in form of a + b root3 where a and b are integers
Answer:
Difference of 2 square
So answer: 13-7sqrt3
/thread
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Chlorophile
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(Original post by PILEDRIV3R WALTZ)
X
Posting solutions is against this subforum's rules. Simply giving an answer won't help the OP understand this problem.

(Original post by Abbie :))
I'd usually do it by rationalising the denominator, this is just a way a friend who was better at maths than myself showed me when I was struggling to understand how to do that.

edit; looking over it I don't even know if his method is mathematically sound :mad:.
I'm not entirely sure I understand it either? It just makes it more complicated and messy and you'll end up having to do the same thing?
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Abbie :)
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(Original post by Chlorophile)
I'm not entirely sure I understand it either? It just makes it more complicated and messy and you'll end up having to do the same thing?
Yeah, but he failed AH Maths after that so I guess I should've went elsewhere for help haha

Got to admit though, I'm struggling to see where difference of two squares comes into this
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Chlorophile
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(Original post by Abbie :))
Yeah, but he failed AH Maths after that so I guess I should've went elsewhere for help haha

Got to admit though, I'm struggling to see where difference of two squares comes into this
Try \frac{5-\sqrt 3}{2+\sqrt 3}\times \frac{2-\sqrt3}{2-\sqrt3}
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Abbie :)
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(Original post by Chlorophile)
Try \frac{5-\sqrt 3}{2+\sqrt 3}\times \frac{2-\sqrt3}{2-\sqrt3}
Aww I've never called that difference of two squares
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cambo211
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Read section 5.

http://www.mathcentre.ac.uk/resource...rds-2009-1.pdf
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Zen-Ali
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(Original post by Abbie :))
...
If you have

(a + b)(a - b) \equiv a^2 - b^2.

You'll notice for those two terms you get the difference of two squared terms; squaring the surd will result in rationalisation and that's why you multiply the numerator and the denominator by the conjugate of the denominator. In the example Chloro gave, you'll notice in the denominator you have an expression of the form

(a + b)(a - b)

This corresponds to the difference of two squares.
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Abbie :)
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(Original post by Zen-Ali)
If you have

(a + b)(a - b) \equiv a^2 - b^2.

You'll notice for those two terms you get the difference of two squared terms; squaring the surd will result in rationalisation and that's why you multiply the numerator and the denominator by the conjugate of the denominator.
I didn't even notice that, thank you!
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unclefred
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(Original post by Abbie :))
Aww I've never called that difference of two squares
This is an absolutely typical question that crops up time and again. If you have a rational expression (P/Q) where Q is of the form a+b✓c then multiply top and bottom by a-b✓c. to get a^2-b^2 c on the bottom. This usually turns out to be a whole number which is easy to ultimately divide by. You then have to successfully negotiate the expansion of the numerator.
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Abbie :)
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(Original post by unclefred)
This is an absolutely typical question that crops up time and again. If you have a rational expression (P/Q) where Q is of the form a+b✓c then multiply top and bottom by a-b✓c. to get a^2-b^2 c on the bottom. This usually turns out to be a whole number which is easy to ultimately divide by. You then have to successfully negotiate the expansion of the numerator.
I don't know where my basic maths skills has went, I'm going to have to dig out S4 work

Oh that's me just realised I've stumbled onto A-level forum (which I thought would be a lot harder than surds) haha

Thank you for the help guys! I'm going to head back home to Scottish Qualifications lol
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PerplexedBird
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(Original post by Chlorophile)
Try \frac{5-\sqrt 3}{2+\sqrt 3}\times \frac{2-\sqrt3}{2-\sqrt3}
Yes, thank-you, I did that but somehow when I expand, the answer is different, could you go further please?
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