## anonymous 4 years ago How do I simplify √2-1 / √2 + 1? The answer is 3-2√2. But I got 1.. D:

1. anonymous

I tried: √2 - 1 √2-1 √2 - 1 ------ = ----- x ------ √2 + 1 √2 + 1 √2 - 1

2. anonymous

can u be clear $\frac{\sqrt{2-1}}{\sqrt{2+1}}$ use conjugates $\huge{\frac{\sqrt{2-1}}{\sqrt{2+1}}*\frac{\sqrt{2-1}}{\sqrt{2-1}} = \frac{(2-1)}{\sqrt{3}} = \frac{1}{\sqrt{3}}}$

3. anonymous

no it's just: √2 - 1 / √2 + 1

4. anonymous

$\huge\frac{\sqrt{2-1}}{\sqrt{2-1}}=1$

5. Mimi_x3

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

6. anonymous

why is the denominator: 2-1?

7. anonymous

and the denominator: 3 - 2√2?

8. EscherichiaRinku

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

9. anonymous

ohh..

10. EscherichiaRinku

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

11. Mimi_x3

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

12. anonymous

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

13. Mimi_x3

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

14. anonymous

ohh, i see.

15. EscherichiaRinku

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

16. anonymous

ohh, thanks guys!

17. anonymous

Mimi, how did you get 3 - 2√2/1? D:

18. anonymous

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

19. Mimi_x3

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.