Maths question

paddyzk · 12-05-2012 08:15PM #1

Was doing the 2011 pre paper and couldn't rap my head round this:

(√5 -1/√2)(√5 +1/√5).Give answer in the form a(1 -1/√b),where a and b are natural numbers.
When I simplify it I get 6 -3√10/5

Indiego · 12-05-2012 10:56PM

paddyzk wrote: »

Was doing the 2011 pre paper and couldn't rap my head round this:

(√5 -1/√2)(√5 +1/√5).Give answer in the form a(1 -1/√b),where a and b are natural numbers.
When I simplify it I get 6 -3√10/5

I just tried it there and ended up with 4.5

Ill give it a proper go for you tomorrow when I'm not half asleep XD

edit: with the aid of a calculator it appear I'm right, but I'm not sure about getting the form they've asked for, ill give it a thinking over XD

edit2: never mind I took it down wrong... sleeping time for me I think..

whiteandlight · 19-05-2012 01:29PM

paddyzk wrote: »

Was doing the 2011 pre paper and couldn't rap my head round this:

(√5 -1/√2)(√5 +1/√5).Give answer in the form a(1 -1/√b),where a and b are natural numbers.
When I simplify it I get 6 -3√10/5

Ok this is tough to write but here goes:
rt5Xrt5 + rt5/rt5 - rt5/rt2 - 1/rt2rt5
5+1- rt5/rt2 -1/rt2rt5
6 - rt5/rt2 -1/rt2rt5. Now get a common denominator which is rt5rt2

{6rt5rt2 - (rt5)(rt5) -(1)(1)}/rt2rt5

{6rt2rt5 - 5 - 1}/rt2rt5
6rt2rt5/rt2rt5 -6/rt2rt5. Now remember rt2rt5 is the same as rt10

6 -6/rt2rt5
= 6(1 - 1/rt10)

A=6 and b=10

If there's any step you don't understand let me know

paddyzk · 19-05-2012 04:24PM

Musicmental85 wrote: »

Ok this is tough to write but here goes:
rt5Xrt5 + rt5/rt5 - rt5/rt2 - 1/rt2rt5
5+1- rt5/rt2 -1/rt2rt5
6 - rt5/rt2 -1/rt2rt5. Now get a common denominator which is rt5rt2

{6rt5rt2 - (rt5)(rt5) -(1)(1)}/rt2rt5

{6rt2rt5 - 5 - 1}/rt2rt5
6rt2rt5/rt2rt5 -6/rt2rt5. Now remember rt2rt5 is the same as rt10

6 -6/rt2rt5
= 6(1 - 1/rt10)

A=6 and b=10

If there's any step you don't understand let me know

Could you explain how √5(1/5) =√5/√5 ?

whiteandlight · 19-05-2012 06:41PM

Where is that or is that a general question? If you mean on the first line it was rt5(1/rt5) not rt5(1/5)

paddyzk · 19-05-2012 07:08PM

Musicmental85 wrote: »

Where is that or is that a general question? If you mean on the first line it was rt5(1/rt5) not rt5(1/5)

Sorry typo on my part.Yeah I meant the first part could you please explain that ?

whiteandlight · 19-05-2012 08:12PM

Thats some very bad hand written on a pad detailed first line or so. Remember that multiplying fractions is top by top, bottom by bottom so the root5's end up cancelling out

paddyzk · 19-05-2012 11:14PM

Musicmental85 wrote: »

Thats some very bad hand written on a pad detailed first line or so. Remember that multiplying fractions is top by top, bottom by bottom so the root5's end up cancelling out

Thanks very much, tis all clear to me now ^^

whiteandlight · 19-05-2012 11:21PM

Here try another to make sure you have it. Its a LC OL question but similar style

And for a real challenge try part three by multiplying without the first two parts as they are helping steps. Best of luck

Maths question

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