Question

need help rationalizing the denominator
\[2ab/\sqrt{5}-1\]

Answer 1

Multiply the numerator and denominator by \[\sqrt{5}\]

Answer 2

so i end up with \[2ab \sqrt{5}/4\]?

Answer 3

Is it \[ \frac{ 2ab }{ \sqrt{5} -1} ?\]

Answer 4

yes

Answer 5

Know about conjugates?

Answer 6

not sure

Answer 7

With surds: two surds are said to be conjugate of each other, if their product gives a difference of their square

Answer 8

So in this case we're multiplying the denominator by it's conjugate, to rationalize it...

Answer 9

Conjugate of \[(\sqrt{5}-1) = (\sqrt{5}+1)\]

Answer 10

Do you understand?

Answer 11

yes

Answer 12

Good, then work it out...

Answer 13

so i should have an answer of 2ab(root5=1) / 6

Answer 14

?

Answer 15

No, try again.

Answer 16

i dont understand how to multiply the \[\sqrt{5}-1\]and \[\sqrt{5}+1\]

Answer 17

You should get\[\frac{ 2ab (\sqrt{5} +1)}{ 4}\]
Reduced to:
\[\frac{ab(\sqrt{5} +1)}{ 2}\]

Answer 18

oh okay so the only thing i was doing wrong was not reducing the fraction?

Answer 19

Okay, multiplying that is trivial. Just expand as before

Answer 20

i see now. so to multiply that i just cancel the root making 5 just 5 and then subtract the 1

Answer 21

yeah

Answer 22

okay thank you very much!

Answer 23

Like this
\[(\sqrt{5}-1)(\sqrt{5}+1)\]
\[5 +\sqrt{5}-\sqrt{5}-1=4\]

Answer 24

You have to pay special attention to the signs. You miss, that everything gets messed up!

Answer 25

Yw. (:

Answer 26

:) great help!!

Answer 27

Can you attempt this?
\[\frac{ 4-8\sqrt{2} }{ 1+\sqrt{2}}\]