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Homework Help: Solving Radical Equations

  1. Jan 9, 2017 #1
    1. The problem statement, all variables and given/known data
    (Square root)-12 -3x - 3 = 0
    Everything underline is supposed to be under the square root sign.

    2. Relevant equations

    3. The attempt at a solution
    (Square root3x +12)2 = (3)2
    3x + 12 = 9
    -12 -12
    3x = -3
    x = -1
    Solution in this learning guide says the answer is -7. So I'm just wondering where I went wrong.
    If anyone knows how to make a square root symbol, please let me know.
  2. jcsd
  3. Jan 9, 2017 #2


    Staff: Mentor

    No. Your equation is ##\sqrt{-12 - 3x} = 3##
    If you square the left side, you get -12 - 3x, not 12 + 3x.
    I get x = -7 as well.
  4. Jan 9, 2017 #3


    Staff: Mentor

    BTW, I changed your thread title from "Solving Ration Equations" to "Solving Radical Equations."
    Yours is not a rational equation, which would involve a quotient of two polynomials.
  5. Jan 9, 2017 #4
  6. Jan 9, 2017 #5
    I thought you couldn't square a negative number?
  7. Jan 9, 2017 #6
    there is no square root of a negative number, no even nth root of any negative number
    there are odd nth roots of negative numbers...

    eg square root of -1 is not a real number, but cube root of -1 is -1.
  8. Jan 9, 2017 #7
    So as long as there are undefined units then you can square it?
  9. Jan 9, 2017 #8
    Sorry If I am confusing, all variables like X Y evaluate to a number, the squaring of a negative number is positive.

    The square root or even nth root of a negative number is not defined in terms of a real number.

    You can square a negative number to get a positive.

    -1 *-1 = 1.

    sQAURE ROOT =/= squaring.
  10. Jan 9, 2017 #9
    Ohhh, duh. Sorry! I understand now.
  11. Jan 9, 2017 #10

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Of course you can square a negative number. That is why an equation like ##x^2 = 9## has two solutions: ##x = 3## and ##x = -3##. Both give 9 when you square them.

    Perhaps you meant that you cannot take the square root of a negative number (in the real number system). But in the complex number field we can very nicely take the square root of a negative number, to get a so-called imaginary number. (It might surprise you to know that such things are used all the time by physicists and electrical engineers, among others.)
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