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anonymous

  • 4 years ago

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

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  1. anonymous
    • 4 years ago
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    I tried: √2 - 1 √2-1 √2 - 1 ------ = ----- x ------ √2 + 1 √2 + 1 √2 - 1

  2. anonymous
    • 4 years ago
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    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
    • 4 years ago
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    no it's just: √2 - 1 / √2 + 1

  4. anonymous
    • 4 years ago
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    \[\huge\frac{\sqrt{2-1}}{\sqrt{2-1}}=1\]

  5. Mimi_x3
    • 4 years ago
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    \[\large \frac{\sqrt{2}-1}{\sqrt{2}+1} *\frac{\sqrt{2}-1}{\sqrt{2}-1} = \frac{(\sqrt{2}-1)(\sqrt{2}-1)}{2-1} = \frac{3-2\sqrt{2}}{1} =3-2\sqrt{2} \]

  6. anonymous
    • 4 years ago
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    why is the denominator: 2-1?

  7. anonymous
    • 4 years ago
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    and the denominator: 3 - 2√2?

  8. EscherichiaRinku
    • 4 years ago
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    (a+b)(a-b)=a^2+b^2

  9. anonymous
    • 4 years ago
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    ohh..

  10. EscherichiaRinku
    • 4 years ago
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    and the nominator is (a-b)(a-b) = (a-b)^2 expanded into a^2-2ab+b^2

  11. Mimi_x3
    • 4 years ago
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    because \((\sqrt{a}+\sqrt{b})(\sqrt{a}-\sqrt{b}) = a - b\)

  12. anonymous
    • 4 years ago
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    ohh, thank you! I have to memorize those right?

  13. Mimi_x3
    • 4 years ago
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    hm..if you want to lol. You can use FOIL to work it out anyway, might be harder; depends on you xD

  14. anonymous
    • 4 years ago
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    ohh, i see.

  15. EscherichiaRinku
    • 4 years ago
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    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
    • 4 years ago
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    ohh, thanks guys!

  17. anonymous
    • 4 years ago
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    Mimi, how did you get 3 - 2√2/1? D:

  18. anonymous
    • 4 years ago
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    'cause don't I have to multiply: √2*√2*√2*-1?

  19. Mimi_x3
    • 4 years ago
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    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.

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