Find each product or quotient. Simplify the answers. √-30 / √-10

Key Concepts

Complex Numbers

Complex numbers are numbers that have a real part and an imaginary part, typically expressed in the form a + bi, where 'i' is the imaginary unit defined as √-1. In the context of square roots of negative numbers, such as √-30 and √-10, we express these roots using 'i' to indicate their imaginary nature, allowing us to perform arithmetic operations on them.

Properties of Square Roots

The properties of square roots state that √(a/b) = √a / √b and √(a * b) = √a * √b. These properties are essential for simplifying expressions involving square roots, especially when dealing with products or quotients of square roots, as they allow us to break down complex expressions into simpler components.

Simplification of Expressions

Simplification of expressions involves reducing an expression to its simplest form, which often includes combining like terms, factoring, and rationalizing denominators. In the case of the expression √-30 / √-10, simplification will involve expressing the square roots in terms of complex numbers and then performing the division to arrive at a more manageable form.