Find each product or quotient. Simplify the answers. √-13 * √-13

Key Concepts

Imaginary Numbers

Imaginary numbers are defined as multiples of the imaginary unit 'i', where i is the square root of -1. This concept is crucial when dealing with square roots of negative numbers, as they cannot be expressed as real numbers. For example, √-1 is represented as 'i', and thus √-13 can be simplified to √13 * i.

Properties of Exponents

The properties of exponents govern how to manipulate expressions involving powers. When multiplying like bases, you add the exponents, and when squaring a product, you square each factor. In the case of √-13 * √-13, you can apply the property that states (√a)² = a, leading to the simplification of the expression.

Simplifying Radical Expressions

Simplifying radical expressions involves reducing the expression to its simplest form, often by factoring out perfect squares or using properties of radicals. In this case, √-13 * √-13 simplifies to (√-13)², which equals -13, demonstrating how to handle and simplify products of square roots.