(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that |x| = sqrt(x^2)

3. The attempt at a solution

I've written two proofs but I don't know if they can be justified as real proofs or whether they are valid or not.

Proof 1:

[itex] \surd x^{2} = \surd \vert x \vert ^{2} = \vert x \vert [/itex]

Proof 2:

First Case ) Suppose [itex] x \geq 0 [/itex] then [itex] \surd x^{2} = x = \vert x \vert [/itex]

Second Case ) Suppose [itex] x < 0 [/itex] then [itex] \surd x^{2} = -x [/itex] where [itex] -x > 0 [/itex] therefore [itex]-x = \vert x \vert [/itex]

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# Homework Help: Abs(x) = sqrt(x^2) Proof

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