Why does $\sqrt{x^2}=|x|$?
60261
Is $\sqrt{x^2}=|x|$ or $=x$? Isn't $(x^2)^\frac12=x?$
96204
Irrational number $\sqrt2$ proof
7463
Square root of a square
103987
What does the square root of minus $i$ equal?
101326
My teacher describes absolute value confusingly: $|x|=\pm x,\quad \text{if}\enspace x>0 $.
133496
is $\sqrt{x}$ always positive?
43453
Is ${\sqrt2^{\sqrt2^{\sqrt2^{\sqrt2^\sqrt2}}}}^{...}=4$ correct?
54030
Square and square root and negative numbers
138193
Why is $\sqrt {12} = 2 \sqrt 3$?
37189
Exponent of a number is a square root?
67588
Why does $|e^{ix}|^2 = 1$?
113168
If $a > b$, is $a^2 > b^2$?
3712
Why $\sqrt{-1 \cdot {-1}} \neq \sqrt{-1}^2$?
5747
$\cos(\arcsin(x)) = \sqrt{1 - x^2}$. How?
102138
Why does $\sqrt{x^2}$ seem to equal $x$ and not $|x|$ when you multiply the exponents?
146180
Prove that $x\sqrt{1-x^2} \leq \sin x \leq x$
34913
Why does basic algebra provide one value for $x$ when there should be two?