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Jamierox4ev3r

  • one year ago

Math Review Day 2! 6a. Rationalize the expression and simplify

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  1. Jamierox4ev3r
    • one year ago
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    Give me a second while I type out the expression. Thank you

  2. Jamierox4ev3r
    • one year ago
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    \(\huge\frac{\sqrt{10}}{\sqrt{5}-2}\)

  3. anonymous
    • one year ago
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    do you know the root of ten?

  4. Jamierox4ev3r
    • one year ago
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    yes. The root of 10 is not rational, so I don't see how knowing that would help me solve this problem

  5. Jamierox4ev3r
    • one year ago
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    \(\huge\sqrt{10} = 3.16227766...\)

  6. Jamierox4ev3r
    • one year ago
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    I have a very limited recollection on rationalizing. So an explanation on that would be nice as well, thank you

  7. anonymous
    • one year ago
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    i learned that you can use a perfect number to minimalize something like this heres an example the root of 18 equals 3root2

  8. nincompoop
    • one year ago
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    do you want to see if you can do anything by multiplying it by a conjugate

  9. Jamierox4ev3r
    • one year ago
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    a conjugate...so like the opposite? do you mean multiplying by \(\huge\sqrt{5}+2\) ??

  10. Jamierox4ev3r
    • one year ago
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    o-o

  11. anonymous
    • one year ago
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    |dw:1440462611069:dw|

  12. nincompoop
    • one year ago
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    yes, so in effect if you multiply your original expression by \(\huge \frac{\sqrt{5}+2}{\sqrt{5}+2} \) you are in effect multiplying by 1, which does not change the original expression.

  13. anonymous
    • one year ago
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    root of 30 is irrational

  14. Jamierox4ev3r
    • one year ago
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    okay.... but what would that accomplish? you're not really getting rid of the denominator by doing that, at least i don't think

  15. nincompoop
    • one year ago
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    is that denominator \(\huge \sqrt{5}-2~ or~ \sqrt{5-2}\)

  16. Jamierox4ev3r
    • one year ago
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    wait lemme check mein textbook

  17. Jamierox4ev3r
    • one year ago
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    it is definitely \(\huge\sqrt{5}-2\)

  18. nincompoop
    • one year ago
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    Then try multiplying by conjugate and see what it will yield. you will find out if it will do anything cool or not

  19. anonymous
    • one year ago
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    |dw:1440462940673:dw|

  20. nincompoop
    • one year ago
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    what happens when you multiply a binomial expression by its conjugate? let me show you an example \((a+b) \times (a-b) = a^2-b^2 \) you lose the middle term in a typical trinomial giving you binomial expression still. Here's the fun part, what does the squared term does to a square root?

  21. Jamierox4ev3r
    • one year ago
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    oh right! inverses :S

  22. anonymous
    • one year ago
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    all i can say is that your answer will always be irrational so you have to work your way through the roots

  23. nincompoop
    • one year ago
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    let me show you another example \((\sqrt{2} +3) \times (\sqrt{2}-3) = 2-9 = 7 \)

  24. nincompoop
    • one year ago
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    oops -7 not 7 haha

  25. Jamierox4ev3r
    • one year ago
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    right, so there wouldn't be a root over the two any more

  26. Jamierox4ev3r
    • one year ago
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    I recall that rule: \[\sqrt{x^{2}}\] = x

  27. nincompoop
    • one year ago
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    see the cool stuff multiplying by conjugate does? it gives you a whole new other possibilities such as rationalizing your denominator

  28. Jamierox4ev3r
    • one year ago
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    i see i see.

  29. anonymous
    • one year ago
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    you could do|dw:1440463196135:dw|

  30. Jamierox4ev3r
    • one year ago
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    how would you multiply on the numerator though?

  31. anonymous
    • one year ago
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    ur answer is 2root10 plus 5root2

  32. nincompoop
    • one year ago
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    you multiply it like any root multiplication \(\sqrt{2} \times \sqrt{5} = \sqrt{2 \times 5} =\sqrt{10} \)

  33. anonymous
    • one year ago
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    @nincompoop ur making it way harder than it is

  34. nincompoop
    • one year ago
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    \(\sqrt{5} \times \sqrt{10} = \sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5 \sqrt{2} \)

  35. anonymous
    • one year ago
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    heres the answer \[2\sqrt{10}+5\sqrt{2}\]

  36. Jamierox4ev3r
    • one year ago
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    Oh I see. so you basically simplified \(\sqrt{50}\) Down to \(5\sqrt{2}\). I understand that

  37. nincompoop
    • one year ago
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    yeeeeee now try your own problem

  38. Jamierox4ev3r
    • one year ago
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    as for the \(2\sqrt{10}\), that's just 2 x \(\sqrt{10}\). Got it!

  39. nincompoop
    • one year ago
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    Do not pay attention to those people that only give you answers. Those kind of people do not encourage intellectual growth.

  40. anonymous
    • one year ago
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    well you make everything way harder than it already is

  41. Jamierox4ev3r
    • one year ago
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    so lol hunter you were right. Sorry, I liked how nine explained better. and yeah nin, i know. I like to reach an understanding, I think that's vital for my learning (or in this case, review)

  42. Jamierox4ev3r
    • one year ago
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    *nin oops my bad

  43. anonymous
    • one year ago
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    i'd just help the person that let him get an F

  44. anonymous
    • one year ago
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    *than

  45. Jamierox4ev3r
    • one year ago
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    *then and that's not a good philosophy

  46. nincompoop
    • one year ago
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    get an F and learn your lesson and try HARDER next time... being bailed out does not necessarily mean helping that person understand anything, because you may just be compounding the lack of skills that should have been developed to proceed to the next level.

  47. anonymous
    • one year ago
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    i already had this thing during my whole life: they said its my fault that they got an F and i got beat up for it

  48. Jamierox4ev3r
    • one year ago
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    in fact, getting temporarily "bailed out" will actually damage you in the long run. hoo boy let me tell ya

  49. nincompoop
    • one year ago
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    enough bs in the thread. move on to the next question

  50. Jamierox4ev3r
    • one year ago
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    Anyhow, I'm closing this. Thank you for your thorough explanation @nincompoop and @GTA_Hunter35 try not to provide answers in the future. Thanks

  51. anonymous
    • one year ago
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    if u guys have a problem then deal with it because someone broke my hand because i didn't give him an answer

  52. anonymous
    • one year ago
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    scru dis

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