Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Callisto

Tutor question #1 Simplify the following: \[\frac{1}{\sqrt2 + \sqrt3 + \sqrt5}\] (conditions: pen, paper, no calculator, done in 2 minutes) *

  • one year ago
  • one year ago

  • This Question is Closed
  1. Callisto
    Best Response
    You've already chosen the best response.
    Medals 5

    I got \[ \frac{2\sqrt3 + 3\sqrt2 - \sqrt{30}}{12}\] Was that right?

    • one year ago
  2. RaphaelFilgueiras
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

    • one year ago
  3. apoorvk
    Best Response
    You've already chosen the best response.
    Medals 0

    HUNDRED PERCENT!!!!!!!!!!!!!

    • one year ago
  4. Callisto
    Best Response
    You've already chosen the best response.
    Medals 5

    But it looks so messy...

    • one year ago
  5. bronzegoddess
    Best Response
    You've already chosen the best response.
    Medals 0

    i got something different: isn't it you cant have radicals under a fraction so you multiply by the conjugate?

    • one year ago
  6. Callisto
    Best Response
    You've already chosen the best response.
    Medals 5

    That's what rationalise means

    • one year ago
  7. apoorvk
    Best Response
    You've already chosen the best response.
    Medals 0

    Not messy at all, this is the only way to go about it.

    • one year ago
  8. bronzegoddess
    Best Response
    You've already chosen the best response.
    Medals 0

    yes but if you multiply 1 by the conjugate pair you get the conjugate pair.. your numerator seems wrong..

    • one year ago
  9. Callisto
    Best Response
    You've already chosen the best response.
    Medals 5

    Can you correct it?

    • one year ago
  10. bronzegoddess
    Best Response
    You've already chosen the best response.
    Medals 0

    otherwise can someone please show me a step by step to how you got that answer? and i'll show you what i did :)

    • one year ago
  11. Callisto
    Best Response
    You've already chosen the best response.
    Medals 5

    luckily, I haven't deleted that.. \[(\sqrt2 + \sqrt3 + \sqrt5)(\sqrt2 + \sqrt3 - \sqrt5)\]\[ = (\sqrt2 + \sqrt3)^2-5\]\[ = 2 + 3 + 2\sqrt6-5\]\[=2\sqrt6\] \[\frac{1}{\sqrt2 + \sqrt3 + \sqrt5}\]\[ = \frac{\sqrt2 + \sqrt3 - \sqrt5}{(\sqrt2 + \sqrt3 + \sqrt5)(\sqrt2 + \sqrt3 - \sqrt5)}\]\[ = \frac{\sqrt2 + \sqrt3 - \sqrt5}{2\sqrt6}\]\[ = \frac{2\sqrt3 + 3\sqrt2 - \sqrt{30}}{12}\]

    • one year ago
  12. RaphaelFilgueiras
    Best Response
    You've already chosen the best response.
    Medals 0

    \[1/(\sqrt{2}+\sqrt{3}+\sqrt{5})=1/(a+\sqrt{5})=(a-sqrt{5})/(a^{2}-5)\] \[(\sqrt{2}+\sqrt{3}-\sqrt{5})/(5-5+\sqrt{6})\] \[\sqrt{2}+\sqrt{3}-\sqrt{5}/2\sqrt{6}=2.\sqrt{3}+2.\sqrt{2}-\sqrt{30}/12\]

    • one year ago
  13. bronzegoddess
    Best Response
    You've already chosen the best response.
    Medals 0

    I ended at the second to last step... where did you get the 2 in front of the radicals if you are multiplying by 1?

    • one year ago
  14. Callisto
    Best Response
    You've already chosen the best response.
    Medals 5

    see the first part of it..

    • one year ago
  15. RaphaelFilgueiras
    Best Response
    You've already chosen the best response.
    Medals 0

    5-5+2sqrt(6)*

    • one year ago
  16. RaphaelFilgueiras
    Best Response
    You've already chosen the best response.
    Medals 0

    second line

    • one year ago
  17. Callisto
    Best Response
    You've already chosen the best response.
    Medals 5

    @RaphaelFilgueiras The second term of the numerator is 3\sqrt{2} ?! \sqrt{18} = \sqrt{9 times 2} = 3\sqrt2 ...

    • one year ago
  18. bronzegoddess
    Best Response
    You've already chosen the best response.
    Medals 0

    okay, so the you rationalized the second to last line because of the radical at the bottom?

    • one year ago
  19. Callisto
    Best Response
    You've already chosen the best response.
    Medals 5

    Of course! That's 'rationalise'

    • one year ago
  20. bronzegoddess
    Best Response
    You've already chosen the best response.
    Medals 0

    okay sorry, then you are right.. I just wanted to know where I went wrong...

    • one year ago
  21. RaphaelFilgueiras
    Best Response
    You've already chosen the best response.
    Medals 0

    no in my solution i put (5-5+sqrt(5))(WRONG) instead(5-5+2sqrt(5))

    • one year ago
  22. Callisto
    Best Response
    You've already chosen the best response.
    Medals 5

    Sorry, but I don't know what you're doing.. No offense.

    • one year ago
  23. Callisto
    Best Response
    You've already chosen the best response.
    Medals 5

    Do you mind re-type it again?

    • one year ago
  24. RaphaelFilgueiras
    Best Response
    You've already chosen the best response.
    Medals 0

    i did same as you,but call(a=sqrt(2)+sqrt(3))

    • one year ago
  25. Callisto
    Best Response
    You've already chosen the best response.
    Medals 5

    Okay, and the answer is the same?

    • one year ago
  26. RaphaelFilgueiras
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

    • one year ago
  27. Callisto
    Best Response
    You've already chosen the best response.
    Medals 5

    Okay, thanks everyone!!!

    • one year ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.