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Anguyennn

  • one year ago

How to evaluate √2/3?

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  1. anonymous
    • one year ago
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    is it \[\frac{ \sqrt{2} }{ 3 }\]

  2. Anguyennn
    • one year ago
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    yes

  3. jackthegreatest
    • one year ago
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    just think of it as \[\sqrt{2} \times \frac{ 1 }{ 3 }\]

  4. anonymous
    • one year ago
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    It's an irrational number, it cannot be evaluated, you can only approximate it, \[\sqrt{2} \approx 1.4142\] so we have \[\frac{\sqrt{2}}{3} \approx \frac{1.414}{3}=0.471333....\]

  5. Anguyennn
    • one year ago
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    are you sure?

  6. anonymous
    • one year ago
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    Usually even upto 3 decimal digits is a good approximation if required

  7. Anguyennn
    • one year ago
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    then what about 3/√3

  8. Anguyennn
    • one year ago
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    how would you evaluate this?

  9. Anguyennn
    • one year ago
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    |dw:1442687878850:dw|

  10. anonymous
    • one year ago
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    \[\frac{3}{\sqrt{3}}=\frac{\sqrt{3}\sqrt{3}}{\sqrt{3}}=\sqrt{3} \approx 1.732\]

  11. anonymous
    • one year ago
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    Notice that if you square 1.732, you get \[(1.732)^2=2.999824 \neq 3\]

  12. anonymous
    • one year ago
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    So it is only an approximation

  13. Anguyennn
    • one year ago
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    but at the back of my answers it is showing √3 as the answer

  14. anonymous
    • one year ago
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    |dw:1442698187908:dw| \[\frac{ \sqrt{2} }{ 3 }=\frac{ 1.414 }{ 3 }=0.471 \approx\]

  15. anonymous
    • one year ago
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    That is the exactl answer, \[\sqrt{3}\] is the exact answer \[1.732\] is an approximation, if someone asks what is the answer you'd say \[\sqrt{3}\] but if you for example need a value, you can use an approximate value

  16. Anguyennn
    • one year ago
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    I know that you multiply the denominator by √3 and the numerator as well but how do you get the answer as √3?

  17. anonymous
    • one year ago
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    \[\frac{3}{\sqrt{3}}=\frac{(\sqrt{3})^2}{\sqrt{3}}=(\sqrt{3})^{2-1}=(\sqrt{3})^{1}=\sqrt{3}\]

  18. anonymous
    • one year ago
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    you simply cancel a factor of root 3

  19. Anguyennn
    • one year ago
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    how did you get (√3)^2?

  20. anonymous
    • one year ago
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    3 can be thought of the square of square root of 3, just like how you can write for example 10 as 2 times 5, I've written 3 as root 3 times root 3, or square of root 3 \[3=\sqrt{3} \times \sqrt{3}=\sqrt{9}=(\sqrt{3})^2\]

  21. Anguyennn
    • one year ago
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    ohh ok

  22. Anguyennn
    • one year ago
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    oh ok thank you i get it now thank you

  23. anonymous
    • one year ago
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    You're welcome

  24. Anguyennn
    • one year ago
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    could you help me with one more math problem?

  25. anonymous
    • one year ago
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    sure

  26. Anguyennn
    • one year ago
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    hello?

  27. Anguyennn
    • one year ago
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    r u still there?

  28. anonymous
    • one year ago
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    yep I'm here

  29. Anguyennn
    • one year ago
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  30. anonymous
    • one year ago
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    Ok, show me your attempt or where you are having a problem

  31. Anguyennn
    • one year ago
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    Like I know that you can simplify the 8 by doing √4x2

  32. Anguyennn
    • one year ago
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    I just don't know how to do the cubed root

  33. anonymous
    • one year ago
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    Ok, let's see Suppose I have |dw:1442689623211:dw| The number outside the radical, which tell which root you have to find, you have to pair up factors that many times inside a root to take them out For example |dw:1442689712453:dw||dw:1442689797599:dw| Now let's suppose a slightly more difficult example |dw:1442689856316:dw|

  34. anonymous
    • one year ago
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    another example |dw:1442690185880:dw|

  35. Anguyennn
    • one year ago
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    ohh!!!

  36. Anguyennn
    • one year ago
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    makes sense, but what about the second part because its a negative 27

  37. anonymous
    • one year ago
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    That's slightly tricky! |dw:1442690403700:dw|

  38. anonymous
    • one year ago
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    @Anguyennn you there?

  39. anonymous
    • one year ago
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    |dw:1442691246474:dw|

  40. Anguyennn
    • one year ago
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    hello? i am so sorry the computer was frozen and i did not know how to get back to it until now. i apologize

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