Maths question

paddyzk

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

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

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

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

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

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

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

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

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