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About square root

  1. Apr 22, 2015 #1
    hi guys
    i know all square root and any root(cubic......) rules

    sqrt(x)=x^(1/2)
    sqrt(x^2)=abs(x)
    sqrt(xy)=sqrt(x)*sqrt(y)
    sqrt(x/y)=sqrt(x)/sqrt(y)
    sqrt(-x)=isqrt(x)
    f'(x)=1/2sqrt(x)
    F(x)=2/3*(x^3/2)
    ..............
    my question is:
    is there any rules for this sqrt(x+y)
    or sqrd(x-y)??

    any help please??
     
  2. jcsd
  3. Apr 22, 2015 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    No, there is no way to simplify a square root (or other root) of a sum or difference.

    It's simply a case of "multiplication and addition do not play well together!"
     
  4. Apr 22, 2015 #3
    Yes of course.
    Yesterday i was searching about this(sqrt(x+y)),i found nothing.
    you are right there is no rule for this sqrt(x+y)
    thanks for help friend.
     
  5. Apr 22, 2015 #4

    Mark44

    Staff: Mentor

    You should be aware that there are restrictions on x and y; namely, both must be nonnegative. I.e., x ≥ 0 and y ≥ 0. Without these restrictions you get nonsense like ##1 = \sqrt{1} = \sqrt{-1 * -1} = \sqrt{-1} * \sqrt{-1} = i * i = -1##
    There are restrictions here, as well, with x ≥ 0 and y > 0.
    Not true. For example, if x = -4, then ##\sqrt{-(-4)} = \sqrt{4} = 2##. ##i\sqrt{-4} = i * (2i) = 2i^2 = -2##.
    Here you seem to be tacitly assuming that -x will be negative, which is not true in general.
     
  6. Apr 22, 2015 #5
    Friend:i know all the rules you wrote.
    i was too busy to write them all(in my question).
    But if you really want to help me,find a rule for this sqrt(x+y).
     
  7. Apr 22, 2015 #6
    Forgive me!, i was busy and hurry.
     
  8. Apr 22, 2015 #7

    Mark44

    Staff: Mentor

    There is no such rule.

    Period.
     
  9. Apr 22, 2015 #8
    You are right.
     
  10. Apr 24, 2015 #9

    micromass

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    2016 Award

  11. Apr 25, 2015 #10
    That helps.
    thank you for help,i will read it later!!
     
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