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pratu043

  • 2 years ago

How do you find the rationalising factor of root2 + root7 - root10?

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  1. pratu043
    • 2 years ago
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    |dw:1344951900463:dw|

  2. mathslover
    • 2 years ago
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    multiply that by its conjugate @pratu043 what do you get?

  3. pratu043
    • 2 years ago
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    By conjugate you mean: |dw:1344952032255:dw|

  4. mathslover
    • 2 years ago
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    \[\large{(\sqrt{2}+\sqrt{7}-\sqrt{10})(\sqrt{2}+\sqrt{7}+\sqrt{10})=?}\]

  5. mathslover
    • 2 years ago
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    |dw:1344952080072:dw|

  6. mathslover
    • 2 years ago
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    @pratu043 what do you get by multiplying that.. ?

  7. pratu043
    • 2 years ago
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    How do you find the conjugate?

  8. pratu043
    • 2 years ago
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    I only know how to find for binomial surds.

  9. mathslover
    • 2 years ago
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    @pratu043 let the expression given be like this: \[\large{(\sqrt{2}+\sqrt{7})-(\sqrt{10})}\]

  10. mathslover
    • 2 years ago
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    I meant to say that: a+b-c = (a+b)-(c) right?

  11. pratu043
    • 2 years ago
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    yes

  12. mathslover
    • 2 years ago
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    |dw:1344952309566:dw|

  13. pratu043
    • 2 years ago
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    |dw:1344952351465:dw| What do you do with - root10?

  14. pratu043
    • 2 years ago
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    |dw:1344952415376:dw| sorry

  15. mathslover
    • 2 years ago
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    ok leave that for once... what will be the conjugate of a+b ?

  16. pratu043
    • 2 years ago
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    a-b

  17. mathslover
    • 2 years ago
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    right so let a = c+d and b = b now can u tell me what will be the new conjugate? : (c+d)+(b) conjugate = ?

  18. pratu043
    • 2 years ago
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    (c+d) - (b)

  19. mathslover
    • 2 years ago
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    right so what will be the conjugate of : \[\large{(\sqrt{2}+\sqrt{7})-(\sqrt{10})}\]

  20. pratu043
    • 2 years ago
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    |dw:1344952630671:dw| ok, I got the conjugate part.

  21. mathslover
    • 2 years ago
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    right now : multiply this conjugate with original expression

  22. pratu043
    • 2 years ago
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    |dw:1344952686106:dw| right?

  23. mathslover
    • 2 years ago
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    good so we have: \[\large{2\sqrt{14}-1}\] now:(√2 + √7 - √10)[(√2 + √7 + √10) (2√14 + 1)] do this

  24. pratu043
    • 2 years ago
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    |dw:1344952926110:dw|

  25. pratu043
    • 2 years ago
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    But why should we do this?

  26. mathslover
    • 2 years ago
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    it is a step towards the answer

  27. mathslover
    • 2 years ago
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    also try to check that out pratu that u did: can that be more simplified?

  28. mathslover
    • 2 years ago
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    @pratu043 you there?

  29. pratu043
    • 2 years ago
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    sorry yes i am there.

  30. pratu043
    • 2 years ago
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    do you mean that we should try and convert the irrationals in that expression to mixed surds?

  31. mathslover
    • 2 years ago
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    yes

  32. pratu043
    • 2 years ago
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    I think I can handle it on my own now, thanks!!

  33. mathslover
    • 2 years ago
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    (√2 + √7 - √10)[(√2 + √7 + √10) (2√14 + 1)] \[\large{(\sqrt{2}+\sqrt{7}-\sqrt{10})(\sqrt{2}+\sqrt{7}+\sqrt{10})(2\sqrt{14}+1)}\] \[\large{(9+2\sqrt{14}-10)(2\sqrt{14}+1)=(2\sqrt{14}-1)(2\sqrt{14}+1)=56-1=55}\]

  34. mathslover
    • 2 years ago
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    nice to hear best of luck

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