Question

How do I simplify √2-1 / √2 + 1? The answer is 3-2√2. But I got 1.. D:

Answer 1

I tried:

√2 - 1 √2-1 √2 - 1
------ = ----- x ------
√2 + 1 √2 + 1 √2 - 1

Answer 2

can u be clear
\[\frac{\sqrt{2-1}}{\sqrt{2+1}}\]
use conjugates

\[\huge{\frac{\sqrt{2-1}}{\sqrt{2+1}}*\frac{\sqrt{2-1}}{\sqrt{2-1}} = \frac{(2-1)}{\sqrt{3}} = \frac{1}{\sqrt{3}}}\]

Answer 3

no it's just: √2 - 1 / √2 + 1

Answer 4

\[\huge\frac{\sqrt{2-1}}{\sqrt{2-1}}=1\]

Answer 5

\[\large \frac{\sqrt{2}-1}{\sqrt{2}+1} *\frac{\sqrt{2}-1}{\sqrt{2}-1} = \frac{(\sqrt{2}-1)(\sqrt{2}-1)}{2-1} = \frac{3-2\sqrt{2}}{1} =3-2\sqrt{2} \]

Answer 6

why is the denominator: 2-1?

Answer 7

and the denominator: 3 - 2√2?

Answer 8

(a+b)(a-b)=a^2+b^2

Answer 9

ohh..

Answer 10

and the nominator is (a-b)(a-b) = (a-b)^2 expanded into a^2-2ab+b^2

Answer 11

because \((\sqrt{a}+\sqrt{b})(\sqrt{a}-\sqrt{b}) = a - b\)

Answer 12

ohh, thank you! I have to memorize those right?

Answer 13

hm..if you want to lol.
You can use FOIL to work it out anyway, might be harder; depends on you xD

Answer 14

ohh, i see.

Answer 15

At school we were all forced to memorize such formulas, lol. Well, if you work on enough problems the simplification formulas will be intuitive :D

Answer 16

ohh, thanks guys!

Answer 17

Mimi, how did you get 3 - 2√2/1? D:

Answer 18

'cause don't I have to multiply: √2*√2*√2*-1?

Answer 19

I used FOIL, to do it.
Or you can use \[(\sqrt{a}-\sqrt{b})^{2} = a-2\sqrt{ab} +b\]
I don't know what you are doing there, sorry.