Square Root Part 3

[nycmathguy]

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?

 

[MathLover1]

............... eliminate square root on left side

..........true

Integer solution:

Number line:

 

[nycmathguy]

............... eliminate square root on left side

..........true

Integer solution:

Number line:

Explain the integer solution part of your reply.

 

[MathLover1]

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

 

[nycmathguy]

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

Very cool. I will explore further when time allows.
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