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When to rationalize the denominator?

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1. I already know how to rationalise the denominator, I just want to know when

For example, in this problem:

I have to add the numbers first. But in this problem:

I have to rationalize the first fraction first. Can someone help me out and explain why? Thanks.
2. Is that when you times it all by 1 - (square root) 2 and multiple the whole thing out?
Then after that times the whole thing by (square root 2) and you should get that answer
3. Can you see what would happen if you multiplied top and bottom by
4. (Original post by Gabzinc)
I already know how to rationalise the denominator, I just want to know when

For example, in this problem:

I have to add the numbers first. But in this problem:

I have to rationalize the first fraction first. Can someone help me out and explain why? Thanks.
In the second one, multiply the fraction by
5. (Original post by RDKGames)
In the second one, multiply the fraction by
Probably easier to rewrite as and then rationalise.
6. (Original post by NeverLucky)
Probably easier to rewrite as and then rationalise.
I'd find it easier to rewrite it as then add on . Each to their own I guess.
7. (Original post by NeverLucky)
Can you see what would happen if you multiplied top and bottom by
oh wow xD
So you're saying the denominator here is
and not sqrt 2?
8. Maybe I should ask a better question: why so I add one to the fraction instead of rationalise it first? (at least thats what the mark scheme says)
9. (Original post by Gabzinc)
Maybe I should ask a better question: why so I add one to the fraction instead of rationalise it first? (at least thats what the mark scheme says)
I didn't understand either of your questions...
10. (Original post by RDKGames)
I didn't understand either of your questions...
Sorry, I'm being really confusing :s

In the first question,
$\frac{1}{1+\frac{1}{^{\sqrt{2}}}}$
Usually the first thing I would do is rationalize the 1/√2. Apparently this is wrong, and I am supposed to join the 1 and the 1/√2 first. Just want to know why.

In the second question,

$\frac{6}{\sqrt{3}}+\sqrt{27}$

I tried to add them like I would ordinary fractions. Obviously, this was wrong as well.

In a nutshell, I just want to know when exactly to rationalize the denominator, as I'm clearly doing it wrong :/
11. (Original post by Gabzinc)
Maybe I should ask a better question: why so I add one to the fraction instead of rationalise it first? (at least thats what the mark scheme says)
You can rationalise it first or you can add up the bottom part of the fraction first. It doesn't matter which way you do it - you'll get the same answer either way.
12. (Original post by NeverLucky)
You can rationalise it first or you can add up the bottom part of the fraction first. It doesn't matter which way you do it - you'll get the same answer either way.
Oh... just tried it and it worked, thanks! I think I was rationing incorrectly all this time...
oops.

That's really embarrassing.

Thanks for the help, and sorry for wasting your time !

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