when-do-I-use-x-for-x-2-

Question Number 113901 by frc2crc last updated on 16/Sep/20

w h e n d o I u s e ∣ x ∣

f o r \sqrt{x^{2}} ?

Commented by MJS_new last updated on 16/Sep/20

almost always

p^{2} ⩾ 0 \forall p \in R \Leftrightarrow p^{2} \in R^{+} \forall p \in R

\sqrt{q} ⩾ 0 \forall q \in R^{+}

\Rightarrow \sqrt{p^{2}} ⩾ 0 \forall p \in R

\Rightarrow \sqrt{x^{2}} =∣ x ∣ \forall x \in R

we {don}^{'} t use it in calculus (integral solving

by substitution)

Commented by frc2crc last updated on 16/Sep/20

\sqrt{4} = 2 o r ∣ 2 ∣ ?

Commented by bobhans last updated on 16/Sep/20

\sqrt{4} = 2 a n d ∣ 2 ∣ = 2

Commented by MJS_new last updated on 16/Sep/20

\sqrt{2^{2}} =∣ 2 ∣= 2

\sqrt{{(- 2)}^{2}} =∣ - 2 ∣= 2

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