Surds A level maths question?

[Hello]

I'm revising for my A levels, and was doing fine until i came across this question. It was to rationalise the denominator, simplifying where possible.

I uploaded a photo of what i did to a very very old twitter account of mine, if anyone could have a look? The answer underlined is what i got, however the one circled is what the actual answer is. Can someone explain to me what i've done wrong and how i would get the right answer?
http://twitter.com/HelloJessieJ/status/4...20/photo/1

[Jenn]

(Squareroot 3 + 7)*(squareroot 3 - 7) should give you (squareroot 3 - 7)^2= 3-(14*squareroot 3)+49

[abhi]

actually u did a little mistake while rationalising denominator.
first tell me is it 3 root 3 or cube root of 3???

[Archimedes]

You used an incorrect rationalizing fraction...

your denominator is: (3√3 + 7)

so you should multiply numerator and denominator by the conjugate which is: (3√3 - 7)

to get...

[11(3√3 - 7)]/(27 - 49) = [- 11(7 - 3√3)]/(- 22) = (7 - 3√3)/2

archimedes

[the way you write radical expressions is WRONG ! ]

[M@thM@ni@c]

I would point out the same as Abhi...your original problem at the beginning is not the one you did your solution for. You dropped the 3; whether it is a cubed root or a factor would make a huge difference.

[David]

As some others already pointed out. The original question is:

11 / (3√3 + 7), but then the first 3 somehow got dropped out.

So your √9, should've been 9√9 = 27, then you get the correct answer.