In Exercises 21–32, simplify by factoring. __ √28

Key Concepts

Factoring

Factoring is the process of breaking down an expression into a product of simpler factors. In algebra, this often involves identifying common factors or applying techniques such as grouping, using the distributive property, or recognizing special products. Understanding how to factor is essential for simplifying expressions and solving equations.

Square Roots

A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 28 can be expressed in terms of its prime factors. Recognizing how to simplify square roots by factoring out perfect squares is crucial for simplifying radical expressions.

Prime Factorization

Prime factorization is the process of expressing a number as the product of its prime factors. For instance, the prime factorization of 28 is 2^2 × 7. This concept is important in simplifying square roots, as it allows us to identify and extract perfect squares from under the radical sign, facilitating the simplification process.