Why doesn't $\sqrt{ab}=\sqrt{a}\sqrt{b}$ work for $a,b<0$?
68315
Why doesn't multiplying square roots of imaginary numbers follow $\sqrt{a} \times \sqrt{b} = \sqrt{ab}$?
158335
Why is this $0 = 1$ proof wrong?
31783
Is this proof of $ab = 0$ correct?
59442
Are there $a,b>1$ with $a^4\equiv 1 \pmod{b^2}$ and $b^4\equiv1 \pmod{a^2}$?
111432
Square root of a number squared is equal to the absolute value of that number
150309
Why do we assume $a+b=b+a$ in a Ring with 1. Also, is it true with Rings without 1?
8589
$\sqrt[b_1]{a_1}+\sqrt[b_2]{a_2}+\cdots+\sqrt[b_k]{a_k}$ not an integer
66451
In a ring, how do we prove that a * 0 = 0?
75690
Does the given matrix have a square root?
70660
Why is $\sqrt{8}/2$ equal to $\sqrt{2}$?
67394
How to interpret $\mathbb{P}(B|A)$ when $\mathbb{P}(A) = 0$
147892
Proving if $x<y$ then $\sqrt{x} < \sqrt{y}$
99631
Prove/Disprove: Find $a\in S_4$ that is not a power of $b$ such that $ab=ba$ while $b=(123)$
54952
Is it true that $\limsup\sqrt[n]{|a_n|}=\limsup\sqrt[n]{|a_n-a_{n-1}|}$, ($n>1$), where $\{a_n\}$ does not have a finite limit?
60261
Is $\sqrt{x^2}=|x|$ or $=x$? Isn't $(x^2)^\frac12=x?$
142470
$\mathbb{Q}(\sqrt{p},\sqrt[3]{q})= \mathbb{Q}(\sqrt{p}\cdot \sqrt[3]{q})$ ??
96630
Let a and b be real numbers such that 0  \sqrt{ab} > \frac{2ab}{a + b}$