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Math Question — Parallax Forums

Math Question

LisaQLisaQ Posts: 33
edited 2010-09-20 15:51 in General Discussion
Brushing upon some long forgotten math and came across something I don't understand. The question is how does 8 times the square root of (81- (216/32) ^2) simplify to 18 times the square root of 7? This is from this link:

http://www.khanacademy.org/video/part-1-of-proof-of-heron-s-formula.

Sadly, I've spent about 3 hours manipulating numbers and trying to work it out. Any help is appreciated.

Comments

  • stamptrolstamptrol Posts: 1,731
    edited 2010-09-19 16:08
    I wouldn't call this a simplification, but working both out on a calculator gives 47.623.

    If you don't get the right answer, its likely due to not doing the calcs within the brackets correctly. Divide 216/32 first. Square that answer. subtract from 81. Take the sq.root. Mult by 8. Same as 18 times sq. rt of 7.
    The video actually goes through it quite well.
  • LisaQLisaQ Posts: 33
    edited 2010-09-20 02:39
    Tom,

    I think you misunderstood, I can get the answer on the calculator. 216/32 is equal to 6.75. Then square that to get 45.5625. Next subtract that from 81 to get 35.4375. The sqrt of 35.4375 is 5.95294...multiplied by 8 is 47.6235

    What I am trying to figure out is how to do the problem in radical form, how to get the answer 18sqrt7- not the result of 18 multiplied by sqrt7.

    Thanks,
    Lisa
  • LeonLeon Posts: 7,620
    edited 2010-09-20 03:36
    I don't think that 18*sqrt(7) is actually the answer, that is what needs to be calculated. The approximation is easier to calculate. It's like using Newton-Raphson for calculating square roots and trig functions.
  • stamptrolstamptrol Posts: 1,731
    edited 2010-09-20 05:07
    The 18*sqrt(7) is the answer to a previous problem the guy in the video got. He's using the current example to show that a different method will give the same answer.
  • max72max72 Posts: 1,155
    edited 2010-09-20 05:10
    I would solve it this way.
    remember
    (A^2)*(B^2)=(A*B)^2

    Edit:
    the attached file was extremely small.
    I tried to make it bigger.
    Forum_forumla_bigger.png
    585 x 633 - 165K
  • LisaQLisaQ Posts: 33
    edited 2010-09-20 06:38
    Max,
    Thank you, that was exactly what I was asking for! Thank you everyone for your help.
    Lisa
  • Duane DegnDuane Degn Posts: 10,588
    edited 2010-09-20 15:51
    All those squareroots remind me solving special relativity problems. Break out the butcher paper.

    There's something fun about a really messy algebra problem.

    Duane
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