# Fungrim entry: 0d8e03

$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$
Assumptions:$a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \left(0, \infty\right)$
Alternative assumptions:$a \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \setminus \left(-\infty, 0\right]$
Alternative assumptions:$a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \setminus \left\{0\right\} \;\mathbin{\operatorname{and}}\; \arg(a) - \arg(b) \in \left(-\pi, \pi\right]$
TeX:
\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}

a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \left(0, \infty\right)

a \in \left[0, \infty\right) \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \setminus \left(-\infty, 0\right]

a \in \mathbb{C} \;\mathbin{\operatorname{and}}\; b \in \mathbb{C} \setminus \left\{0\right\} \;\mathbin{\operatorname{and}}\; \arg(a) - \arg(b) \in \left(-\pi, \pi\right]
Definitions:
Fungrim symbol Notation Short description
Sqrt$\sqrt{z}$ Principal square root
CC$\mathbb{C}$ Complex numbers
OpenInterval$\left(a, b\right)$ Open interval
Infinity$\infty$ Positive infinity
ClosedOpenInterval$\left[a, b\right)$ Closed-open interval
OpenClosedInterval$\left(a, b\right]$ Open-closed interval
Arg$\arg(z)$ Complex argument
Pi$\pi$ The constant pi (3.14...)
Source code for this entry:
Entry(ID("0d8e03"),
Formula(Equal(Sqrt(Div(a, b)), Div(Sqrt(a), Sqrt(b)))),
Variables(a, b),
Assumptions(And(Element(a, CC), Element(b, OpenInterval(0, Infinity))), And(Element(a, ClosedOpenInterval(0, Infinity)), Element(b, SetMinus(CC, OpenClosedInterval(Neg(Infinity), 0)))), And(Element(a, CC), Element(b, SetMinus(CC, Set(0))), Element(Sub(Arg(a), Arg(b)), OpenClosedInterval(Neg(Pi), Pi)))))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2020-04-08 16:14:44.404316 UTC