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.

Reply 6

Abbie :)

10

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:

.

(edited 9 years ago)

Reply 7

PILEDRIV3R WALTZ

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

Reply 8

Chlorophile

20

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?

(edited 9 years ago)

Reply 9

Abbie :)

10

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

Reply 10

Chlorophile

20

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}

Reply 11

Abbie :)

10

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 :colondollar:

Reply 12

cambo211

19

Read section 5.

http://www.mathcentre.ac.uk/resources/uploaded/mc-ty-surds-2009-1.pdf

Reply 13

Zen-Ali

8

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.

(edited 9 years ago)

Reply 14

Abbie :)

10

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!

Reply 15

unclefred

4

Original post by Abbie :)

Aww I've never called that difference of two squares :colondollar:

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.

Reply 16

Abbie :)

10

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 :frown:

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