Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

B Squaring both sides of an equation?

  1. Mar 24, 2017 #1
    If I wanted to simplify an equation, say of the form [tex]\sqrt{A} + B = 0[/tex] to get rid of the square root, is it correct to square as is? If so, why would it then be wrong to move one term to the other side before squaring?

    Thanks
     
  2. jcsd
  3. Mar 24, 2017 #2

    Haynes Kwon

    User Avatar
    Gold Member

    Prior to beginning, you must be aware of the possible ranges of A and B.
    I believe this is what you missed.
    A>0 or A=0
    I will assume that B is the component of the set of the entire negative real number.

    If you have learned about how
    (X+Y)^2 is developed,

    X^2+2XY+Y^2,

    you will see that the linear terms of X and Y still remain in the equation.

    Now let's substitute A^(1/2) with P, and B with Q. In order to get rid of square root, every degree of P should be the multiple of 2, or 0.

    P + Q = 0

    If you square both sides of the equation without any transposition, that will be

    P^2+2PQ+Q^2=0

    and you will notice that still there is a linear term of P.

    If you just want to simplify the original equation,

    A=B^2 (A>0 or A=0, B<0 or B=0)


    may be accurate.
     
    Last edited: Mar 24, 2017
  4. Mar 24, 2017 #3

    PeroK

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    What makes you think that would be wrong?
     
  5. Mar 24, 2017 #4

    Haynes Kwon

    User Avatar
    Gold Member

    B must be 0 or a negative number. If he squared with one term moved to other side, he could have got a positive value.
     
    Last edited: Mar 24, 2017
  6. Mar 24, 2017 #5

    PeroK

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    It depends what you want to do. Suppose, for example, ##B = -3##, then your equation becomes:

    ##\sqrt{A} = -B##

    ##A = B^2 = 9##

    Whereas, squaring the original equation doesn't get you very far:

    ##A -6 \sqrt{A}+ 9 = 0##

    Which doesn't really help.
     
  7. Mar 24, 2017 #6

    Mark44

    Staff: Mentor

    If you "square an equation" (really, square both sides of an equation), you should end up with an equation.
    What you have above is missing "= 0".
     
  8. Mar 24, 2017 #7

    Haynes Kwon

    User Avatar
    Gold Member

    Thank you. My bad.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted