Find each product or quotient. Simplify the answers. √-3 * √-8

Key Concepts

Imaginary Numbers

Imaginary numbers are defined as multiples of the imaginary unit 'i', where i is the square root of -1. They arise when taking the square root of negative numbers, which is not possible within the realm of real numbers. For example, √-3 can be expressed as i√3, allowing for operations involving negative square roots.

Properties of Square Roots

The properties of square roots include the product and quotient rules, which state that √a * √b = √(a*b) and √a / √b = √(a/b) for non-negative a and b. These properties can be extended to include imaginary numbers, enabling the simplification of expressions involving square roots of negative values.

Simplification of Expressions

Simplification of expressions involves reducing complex expressions to their simplest form. This includes combining like terms, factoring, and applying mathematical properties. In the context of the given problem, simplifying the product of two imaginary numbers requires careful application of the properties of square roots and the definition of imaginary numbers.