Find each product or quotient. Simplify the answers. √-24 / √8

Key Concepts

Square Roots of Negative Numbers

In algebra, the square root of a negative number involves the imaginary unit 'i', where i = √-1. For example, √-24 can be simplified to √(24) * √(-1) = 2√6 * i. Understanding this concept is crucial for handling expressions that include square roots of negative values.

Simplifying Square Roots

Simplifying square roots involves breaking down the radicand (the number under the square root) into its prime factors and extracting perfect squares. For instance, √8 can be simplified to √(4 * 2) = 2√2. This process is essential for simplifying expressions in algebra.

Division of Complex Numbers

When dividing complex numbers, such as those involving imaginary units, it is important to express the result in a standard form. This often involves multiplying the numerator and denominator by the conjugate of the denominator. In this case, simplifying √-24 / √8 requires careful handling of both real and imaginary components.