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Anguyennn

  • one year ago

how to simplify 2√4-√9?

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  1. jim_thompson5910
    • one year ago
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    What is the square root of 4 equal to?

  2. Anguyennn
    • one year ago
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    2

  3. jim_thompson5910
    • one year ago
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    correct What is the square root of 9 equal to?

  4. Anguyennn
    • one year ago
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    3

  5. Anguyennn
    • one year ago
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    and you multiply 2x2 and minus 3? correct?

  6. jim_thompson5910
    • one year ago
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    so you really have `2*2-3` evaluate that to get ??

  7. jim_thompson5910
    • one year ago
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    correct

  8. Anguyennn
    • one year ago
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    oh ok!! thank you but what about when its √2?

  9. jim_thompson5910
    • one year ago
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    taking the square root of 2 doesn't give a whole number like the square root of 4 does

  10. Anguyennn
    • one year ago
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    like 3√2-5√2-2√2

  11. jim_thompson5910
    • one year ago
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    I don't see a square root of 2 in your problem though

  12. jim_thompson5910
    • one year ago
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    Oh I see now

  13. jim_thompson5910
    • one year ago
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    replace every copy of "square root of 2" with x so you'll have 3x-5x-2x simplify that to get ???

  14. Anguyennn
    • one year ago
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    -4x

  15. Anguyennn
    • one year ago
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    but how come you replaced it with an x?

  16. jim_thompson5910
    • one year ago
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    well you don't need to, but you can think of it like that basically you're combining like terms. In this case, all 3 terms are like terms because they have a root 2 in them

  17. Anguyennn
    • one year ago
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    yes

  18. jim_thompson5910
    • one year ago
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    3x-5x-2x = -4x so you now replace the x with square root of 2 so the final answer is \(\Large -4\sqrt{2}\)

  19. Anguyennn
    • one year ago
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    i am still confused because for other questions it would have different numbers and i don't know how to do them

  20. jim_thompson5910
    • one year ago
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    like what for example?

  21. Anguyennn
    • one year ago
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    √18+√50-√8

  22. jim_thompson5910
    • one year ago
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    have you tried to simplify each root?

  23. Anguyennn
    • one year ago
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    dividing them all by 2?

  24. jim_thompson5910
    • one year ago
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    think of all of the factors of 18 which factors are perfect squares?

  25. Anguyennn
    • one year ago
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    I am not sure

  26. Anguyennn
    • one year ago
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    sorry

  27. jim_thompson5910
    • one year ago
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    factors of 18 1,2,3,6,9,18

  28. Anguyennn
    • one year ago
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    ok

  29. jim_thompson5910
    • one year ago
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    which factor is a perfect square?

  30. Anguyennn
    • one year ago
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    9

  31. jim_thompson5910
    • one year ago
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    so we can say this \[\Large \sqrt{18} = \sqrt{9*2}\] \[\Large \sqrt{18} = \sqrt{9}*\sqrt{2}\] \[\Large \sqrt{18} = 3*\sqrt{2}\]

  32. jim_thompson5910
    • one year ago
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    I factored 18 into 9*2 then I used the rule \[\Large \sqrt{x*y} = \sqrt{x}*\sqrt{y}\]

  33. Anguyennn
    • one year ago
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    yes

  34. jim_thompson5910
    • one year ago
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    now let's do 50 what are the factors of 50?

  35. Anguyennn
    • one year ago
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    1, 2, 5, 10, 25

  36. Anguyennn
    • one year ago
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    and it would be 25 that is the perfect square

  37. jim_thompson5910
    • one year ago
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    yes so 50 = 25*2

  38. jim_thompson5910
    • one year ago
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    what would \(\Large \sqrt{50}\) simplify to?

  39. Anguyennn
    • one year ago
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    √25x2

  40. jim_thompson5910
    • one year ago
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    then break it up using the rule I posted

  41. Anguyennn
    • one year ago
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    √50= √25x2 =√25x √2 5√2

  42. jim_thompson5910
    • one year ago
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    good

  43. jim_thompson5910
    • one year ago
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    now onto 8 the factors of 8 are ???

  44. Anguyennn
    • one year ago
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    1,2,4,8

  45. jim_thompson5910
    • one year ago
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    which is a perfect square?

  46. Anguyennn
    • one year ago
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    √4

  47. jim_thompson5910
    • one year ago
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    so we can say 8 = 4*2

  48. jim_thompson5910
    • one year ago
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    then use that rule

  49. Anguyennn
    • one year ago
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    √8= √4x2 =√4x√2 2√2

  50. jim_thompson5910
    • one year ago
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    so, \[\Large \sqrt{18}+\sqrt{50}-\sqrt{8}\] is the same as \[\Large 3\sqrt{2}+5\sqrt{2}-2\sqrt{2}\]

  51. jim_thompson5910
    • one year ago
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    we can replace all the square root of 2 terms with x \[\Large 3\color{red}{\sqrt{2}}+5\color{red}{\sqrt{2}}-2\color{red}{\sqrt{2}}\] \[\Large 3\color{red}{x}+5\color{red}{x}-2\color{red}{x}\]

  52. Anguyennn
    • one year ago
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    correct

  53. Anguyennn
    • one year ago
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    is that the answer?

  54. jim_thompson5910
    • one year ago
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    not yet

  55. Anguyennn
    • one year ago
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    would you do 3+5-2 now?

  56. Anguyennn
    • one year ago
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    and get 6√2?

  57. jim_thompson5910
    • one year ago
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    very good, that's your final answer

  58. Anguyennn
    • one year ago
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    oh ok thank you so much!

  59. jim_thompson5910
    • one year ago
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    you're welcome

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