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Please help! (C1 mathematics - surds)

Can somebody please help me by explaining how to get the answer? Thank you! :smile:

Express

3(2+√5)
_______
2-√5

in the form b + c√5 where b and c are integers
Original post by AwayWithTheFae
...


Rationalise denominator by difference of two squares.

Good luck. :smile:
Original post by lazy_fish
Rationalise denominator by difference of two squares.

Good luck. :smile:



Thank you!! :smile:
Original post by lazy_fish
Rationalise denominator by difference of two squares.

Good luck. :smile:


Yeah you just do this, I ended up getting:
-27-12root5
which doesn't seem like a usual core 1 exam answer, but I'm pretty sure that's the answer
The denominator is 2 squares ?
Original post by Old_Simon
The denominator is 2 squares ?


When people say by the difference of 2 squares it just means do it against itself, but the opposite form, so part of it will cancel out.
So times 2-root5 by 2+root5 and you get -1 as answer.
Expand The top to get 6+3√5
Then multiply the top and bottom by 2+√5 (the bottom with the sign changed)
to get (12+15+6√5+6√5)/4-5
Simplify to (27+12√5)/-1
-27-12√5
Original post by ImNormal
When people say by the difference of 2 squares it just means do it against itself, but the opposite form, so part of it will cancel out.
So times 2-root5 by 2+root5 and you get -1 as answer.

tx but it doesn't make sense to me
(edited 9 years ago)
Original post by Old_Simon
tx but it doesn't make sense to me

What is it you don't get?
Reply 9
Avatar for davros
davros
16
Original post by Old_Simon
The denominator is 2 squares ?


It becomes the difference of 2 squares if you multiply 2 - root(5) by 2 + root(5).
Original post by davros
It becomes the difference of 2 squares if you multiply 2 - root(5) by 2 + root(5).

Presumably you then need to multiply the numerator by the same thing then ?
Original post by Old_Simon
...


Yes. :smile:
Original post by lazy_fish
Yes. :smile:

Until I see a worked solution I am never going to believe the q has been stated properly.
Original post by Old_Simon
Until I see a worked solution I am never going to believe the q has been stated properly.


Are you even doing c1? If yes, good luck with your coming exams...
Original post by Buffalo_puppy
Expand The top to get 6+3√5
Then multiply the top and bottom by 2+√5 (the bottom with the sign changed)
to get (12+15+6√5+6√5)/4-5
Simplify to (27+12√5)/-1
-27-12√5


Thank you! This really helped :smile:

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