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anonymous

  • 4 years ago

How do I simplify this expression: √3 / √3 + √2? The answer is 3 - √6... how?

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  1. anonymous
    • 4 years ago
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    is sqrt(2) in the denominator?

  2. anonymous
    • 4 years ago
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    no, there's no root 2 in the denominator

  3. ash2326
    • 4 years ago
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    \(\sqrt 3/( \sqrt 3+ \sqrt 2)\) now multiply numerator and denominator by \(\sqrt 3- \sqrt 2\) we have \( \sqrt 3/( \sqrt 3 + \sqrt 2) *( \sqrt 3 - \sqrt 2)/( \sqrt 3 - \sqrt 2)\) we get \[ (3-2 \sqrt 6)/( 3-2)\] or \[3-2\sqrt 6\]

  4. ash2326
    • 4 years ago
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    sorry it'd be \[3-\sqrt 6\]

  5. anonymous
    • 4 years ago
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    why is it 3 - 2√6?

  6. ash2326
    • 4 years ago
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    ignore the 2 int the last two steps

  7. ash2326
    • 4 years ago
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    did you get??

  8. anonymous
    • 4 years ago
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    but why is it 3 - √6? Did you cancel something?

  9. ash2326
    • 4 years ago
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    when we multiplied \(\sqrt 3 -\sqrt 2\) in the numerator and denominator , denominator became 1 . and numerator became \[3-\sqrt 6\]

  10. anonymous
    • 4 years ago
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    can you please show me? I'm still confused about what you just said.. so sorry D:

  11. ash2326
    • 4 years ago
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    |dw:1327812623013:dw|

  12. anonymous
    • 4 years ago
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    It's called multiplying by the conjugate to rationalize the denominator

  13. anonymous
    • 4 years ago
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    I have it on my textbook but it's kind of confusing..

  14. anonymous
    • 4 years ago
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    because (a-b)(a+b)=a^2-b^2. Thus you eliminate the square roots from the denominator

  15. anonymous
    • 4 years ago
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    ohh..

  16. ash2326
    • 4 years ago
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    |dw:1327812809044:dw|

  17. ash2326
    • 4 years ago
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    the numerator will become = 3- \(\sqrt 6\) denominatorw will be = 3-2= 1

  18. ash2326
    • 4 years ago
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    millie did you get ??

  19. anonymous
    • 4 years ago
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    ohhh.. kind of, aww man.

  20. anonymous
    • 4 years ago
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    why did you square it?

  21. ash2326
    • 4 years ago
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    when ever denominator has the form \(\sqrt a\pm \sqrt b\) multiply numerator and denominator by \(\sqrt a\mp \sqrt b\)

  22. anonymous
    • 4 years ago
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    ohh, so the opposite.. and then?

  23. ash2326
    • 4 years ago
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    we'd in the denominator \[(\sqrt 3 + \sqrt 2)*( \sqrt 3 - \sqrt 2)\] so this is in the form of (a+b)*(a-b)= a^2-b^2 so it'll become \[({\sqrt 3}^2 - {\sqrt 2}^2)\] which is 3-2= 1

  24. anonymous
    • 4 years ago
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    ohhh.. it's 3-2= 1? Not 3^2 - 2^2..?

  25. ash2326
    • 4 years ago
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    yeah , square of \(\sqrt a\) = a

  26. anonymous
    • 4 years ago
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    square root of a number squared is the number itself

  27. ash2326
    • 4 years ago
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    milie you got it??

  28. anonymous
    • 4 years ago
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    yes I did! thank you!

  29. ash2326
    • 4 years ago
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    good :)

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