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anonymous

  • 5 years ago

sqrt (1/12) - sqrt (1/27)

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  1. anonymous
    • 5 years ago
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    When you have the sqrt of a fraction, it is the sqrt of the numerator divided by the sqrt of the denominator. Can you convert both expressions to a fraction with denominator 6?

  2. anonymous
    • 5 years ago
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    Yes I can. The first thing you want to do is get the 1's out of the squareroot. \[\sqrt{a/b}=\sqrt{a}/\sqrt{b}\] So \[\sqrt{1/b}=\sqrt{1}/\sqrt{b}=1/\sqrt{b}\]

  3. anonymous
    • 5 years ago
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    o okay

  4. anonymous
    • 5 years ago
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    Does that make sense or did I use too many symbols and make it too long winded?

  5. anonymous
    • 5 years ago
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    no it makes sense thank u!

  6. anonymous
    • 5 years ago
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    The next thing to do is to simplify \(\sqrt{12},\sqrt{27}\)

  7. anonymous
    • 5 years ago
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    do you know how to do that?

  8. anonymous
    • 5 years ago
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    find a common denominator?

  9. anonymous
    • 5 years ago
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    Basically, what he's saying is that 1/sqrt(a) = sqrt(a) / a. This is because you can multiply by sqrt(a)/sqrt(a) and the root on the bottom cancels out, while the 1 on the top becomes sqrt(a). You get sqrt(12)/12 - sqrt(27)/27, and you know how to simplify from there.

  10. anonymous
    • 5 years ago
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    That's probably a simpler way to look at it, I was going to simplify the denominator and then move it to the top.

  11. anonymous
    • 5 years ago
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    But regardless, you need to simplify the radical.

  12. anonymous
    • 5 years ago
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    but they dont reely have a common denominator do they?

  13. anonymous
    • 5 years ago
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    would it be 3 * 4 and 3 * 9 for it?

  14. anonymous
    • 5 years ago
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    In order to simplify a radical like \(\sqrt{12}\), you need to find a square that divides it. In this case, 4 divides 12, so we write \[\sqrt{12}=\sqrt{4}\sqrt{3}=2\sqrt{3}\]

  15. anonymous
    • 5 years ago
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    Right, exactly.

  16. anonymous
    • 5 years ago
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    Would you prefer to move everything to the top and then deal with it or deal with it first, then move it to the top?

  17. anonymous
    • 5 years ago
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    either way is easiest

  18. anonymous
    • 5 years ago
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    i mean whichever way is easiest

  19. anonymous
    • 5 years ago
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    Let's do it the way quantummodulus suggested. Did you understand what they said?

  20. anonymous
    • 5 years ago
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    yes

  21. anonymous
    • 5 years ago
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    Ok. So what have you gotten to so far?

  22. anonymous
    • 5 years ago
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    (sqrt 12/2 sqrt 3) - (sqrt 27/3 sqrt 3)

  23. anonymous
    • 5 years ago
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    Ok, not quite. I think we got you jumbled up a bit. Let's take a step back. First, we're going to do what is called rationalizing the denominator. That is where we multiply the top and the bottom by the denominator. This will get rid of the square root. Do you know how to do this?

  24. anonymous
    • 5 years ago
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    yes

  25. anonymous
    • 5 years ago
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    Ok, so what do you get after rationalizing the denominator?

  26. anonymous
    • 5 years ago
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    i think i square rooted something that didnt need to be sqaure rooted

  27. anonymous
    • 5 years ago
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    so now i have sq rt 12/12 - sqrt 27/27 the denominators not being sqrt

  28. anonymous
    • 5 years ago
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    Yup, perfect. Now, simplify the radical, like you did before.

  29. anonymous
    • 5 years ago
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    on top?

  30. anonymous
    • 5 years ago
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    Yup.

  31. anonymous
    • 5 years ago
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    okay i got 2 sqrt 3/12 - 3 sqrt 3/27

  32. anonymous
    • 5 years ago
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    Right, now cancel and add fractions.

  33. anonymous
    • 5 years ago
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    sqrt 3/6 - sqrt3/9

  34. anonymous
    • 5 years ago
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    Yup, now common denominators and add.

  35. anonymous
    • 5 years ago
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    3/18 - sqrt 6/18

  36. anonymous
    • 5 years ago
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    \(3*\sqrt{3}\) doesn't equal 3, same for the other fraction

  37. anonymous
    • 5 years ago
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    3 sqrt 3/18 - 2sqrt 3/9

  38. anonymous
    • 5 years ago
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    /18

  39. anonymous
    • 5 years ago
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    now just subtract

  40. anonymous
    • 5 years ago
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    sqrt 3/18 is the answer then?

  41. anonymous
    • 5 years ago
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    Yup. So the process is: rationalize the denominator, simplify the radical, simplify fractions

  42. anonymous
    • 5 years ago
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    Sorry about all of the confusion at the beginning.

  43. anonymous
    • 5 years ago
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    oh no that was my fault thank u for all your help thank u!

  44. anonymous
    • 5 years ago
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    You're welcome. Good luck on any other problems.

  45. anonymous
    • 5 years ago
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    \[\sqrt{a}-\sqrt{b} = \sqrt{a-2\sqrt{a*b}+b}\] Plug in 1/12 for a and 1/27 for b and simplify. The result is: \[{\sqrt{1\over 108}} = {1 \over 6\sqrt{3}}\] The formula is obtained by squaring the quantity radical a - radical b, ie: the left side of the formula equation. The first and last terms of the result is a and b respectively. The mid term is negative two times the product of radical a and radical b. Radical a times radical b is equal to the square root of the product of a and b. The final operation is to take the square root of every thing.

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