Square Root Part 3

Discussion in 'Basic Math' started by nycmathguy, Jul 21, 2021.

  1. nycmathguy

    nycmathguy

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    When the square root of a number or term squared is taken, the answer simply comes out of the radicand.

    Sample:

    sqrt{(x + 1)^2} = x + 1

    Can this be the reason? See below.

    sqrt{(x + 1)^2} = [(x + 1)^2]^(1/2).

    The exponents become 1:

    Exponents: 2 (1/2) = 1

    Anything to the first power equals itself.

    Correct?
     
    nycmathguy, Jul 21, 2021
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  2. nycmathguy

    MathLover1

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    [​IMG] ............... eliminate square root on left side

    [​IMG]..........true

    Integer solution: [​IMG]
    Number line:
    [​IMG]


     
    MathLover1, Jul 21, 2021
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  3. nycmathguy

    nycmathguy

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    Explain the integer solution part of your reply.
     
    nycmathguy, Jul 21, 2021
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  4. nycmathguy

    MathLover1

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    [​IMG]
    [​IMG]

    and solutions for abs value (if x positive, and if x is negative)
    x-(x+1)=-1 =>x-x+1=-1=> 1=-1->false if x negative (disregard it)
    or
    x-(-x+1)=-1 =>x+x+1=-1 =>2x=-1-1 =>2x=-2 =>x=-1 =>true if x positive

    so, equation will be true only if [​IMG]
     
    MathLover1, Jul 22, 2021
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  5. nycmathguy

    nycmathguy

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    Very cool. I will explore further when time allows.
    You have two private messages waiting in your PM.
     
    nycmathguy, Jul 22, 2021
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