HELP PLEASE!!! Maths GCSE stuff

[LittleWonder]

DD is stuck in preparation for tomorrow and I haven't a clue - can anyone explain:

sqrt12 + 15
___
sqrt3

can be written in the form p+q sqrt3, where p and q are intigers.

Find The Value of p and q.

I know p is 2 and q is 5, but i don't understand how!

next!

ok

you split the question into two bits

sqrt12/sqrt3 then + 15/sqrt 3

because they are both sqrts, you can put it over the whole of the first bit i.e. over the whole of 12/3 so you can simplify that bit to the sqrt of 4 (i.e. 12/3) which is 2

the other bit 15/sqrt3 as you know it has to end up as q sqrt 3 you multiply that bit by sqrt 3/sqrt 3. So 15/sqrt 3 times sqrt 3/sqrt 3. The top bit becomes 15 sqrt3 and the bottom is 3 (sqrt 3x sqrt 3) and you can simplify the 15/3 which is 5.

so it ends up as sqrt(12/3) + 15sqrt3/(sqrt3xsqrt3) just before you get to

sqrt4+(15sqrt3/3)

2+5sqrt3

good luck to her littlewonder!

thanks so much - I could only get as far as the first part.

actually, thinking about it...probably the way she is taught is to split the 15 into something multiplied by sqrt 3 so 5x3 which can be written 5xsqrt3xsqrt3 and then you'd have that bit on its own over the sqrt3 so

(5xsqrt3xsqrt3)/sqrt3 and then one of the sqrt3 s on top cancels out with the one on the bottom leaving 5xsqrt3 on top.

I don't know how they teach that level maths these days!

Oh, I'll show her that, meanwhile I am going to get some wine! thank you so much again WizzFox

OMG I'm sure dd1 wouldn't know the answer to this. She has been in her bedroom 'revising' all day and won't let anyone in. This is her worst subject. Probably a 'C', hopefully a 'B'. Fingers crossed

While we on the subject, does anyone know how the marks turn into grades, DD is doing the unit 1 paper soon (year 10) and said to get an A* you have to get 29/30 which sounds very high considering the numbers that do get that grade.

Thank you Foxy!!! She had a similar question and was able to do it. She said I must get on here and thank you from us both!!

yippee! marvellous. Hope it all went well for everyone.