A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

ques

  • This Question is Closed
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    why is sqrt{x^2}=|x|?? let f(x)=sqrt{x^2} g(x)=x h(x)=|x| at x= -1 we have f(x)=plus minus 1 g(x)=-1 h(x)=1 clearly it looks like sqrt{x^2}=plus minus x sorry my equation box is giving errors right now so im using this

  2. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1435127988303:dw|

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

    plus minus 2?

  4. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Also |dw:1435128205480:dw|

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

    |dw:1435128362002:dw|

  6. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    we could say the "2nd roots of 4" are "+2 and -2" as both of them when rised to 2nd power give us 4; but if we stick to the definition of sqrt function, we only pick the positive root.

  7. ikram002p
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @Nishant_Garg what is x^2 range ?

  8. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    \(\sqrt{4} = 2\)

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

    I'm confused, doesn't square rooting gives 2 values?

  10. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    By definition, sqrt(x) is always the positive root of x

  11. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    sqrt(x) is a single valued function

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

    I don't understand, that sounds really really wrong

  13. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    do you have definition of sqrt(x) function wid you ?

  14. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    stick to that

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

    Well, idk, I've been doing plus minus x all the time for sqrt of x^2 How do you suppose the equation x^2=4 has 2 solutions then if u only take the positive value?

  16. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    \[x^2=4 \implies x = \pm \sqrt{~4~} = \pm 2\]

  17. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    \[x^2 =3 \implies x=\pm\sqrt{3} \]

  18. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    i think you're confusing sqrt(x) function with the complex roots of x

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

    This is melting my brain, it feels like I've been square rooting wrong the whole time... so is x^2=4 different from x=sqrt{4} ??

  20. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Yes they are not same. \[x = \sqrt{4} \implies x^2=4\] but the converse is not true.

  21. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    \[x^2=4 \implies x=\color{red}{\pm}\sqrt{4}\]

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

    and x=sqrt{4} implies x=2 ONLY ?

  23. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    there wont be any confusion if we take the definition seriosuly and stick to it

  24. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    that is correct \[x=\sqrt{4}\implies x=2\]

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

    and not minus 2

  26. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Yep. sqrt(x) is never negative

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

    This is just bizzare, I always thought sqrt gives plus minus.....It all looks like a different point of view now

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

    then the equation x^2=4 is to be solved like sqrt{x^2}=sqrt{4} implies |x|=2(by definition of sqrt) removing the mod, x=plus minus 2 but for the equation x=sqrt{4} we have x=2(by definition of sqrt)

  29. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Haha ikr! one not so cool thing about mathematics is sometimes we just need to follow rules and stick to definitions even though they seem unintuitive

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

    can u check my post

  31. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    that looks good to me!

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

    so the plus minus is a consequence of the modulus function and not square root

  33. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    modulus function is a consequence of sqrt

  34. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1435129510602:dw|

  35. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    as you said |x|=2 has two solutions

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

    makes sense now but feels a little different :)

  37. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    since we're messing with roots, notice that below is perfectly okay : |dw:1435129597807:dw|

  38. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    but below is wrong : |dw:1435129708335:dw|

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

    should be |X^7|?

  40. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Yes! |x^7| or |x|^7 both are fine

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

    as it has an odd power it can gives negative numbers

  42. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    Exactly! which changes the original function sqrt(x^14) as x^14 is always positive

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

    amazing thanks a lot...

  44. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    np:)

  45. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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.