CONCEPT PREVIEW Perform the operations mentally, and write the answers without doing intermediate steps.(√28 - √14) (√28 + √14)

Verified step by step guidance

1. Recognize that the expression \((\sqrt{28} - \sqrt{14})(\sqrt{28} + \sqrt{14})\) is in the form of \((a - b)(a + b)\), which is a difference of squares.
2. Recall the difference of squares formula: \((a - b)(a + b) = a^2 - b^2\).
3. Identify \(a = \sqrt{28}\) and \(b = \sqrt{14}\) in the expression.
4. Apply the difference of squares formula: \((\sqrt{28})^2 - (\sqrt{14})^2\).
5. Calculate \((\sqrt{28})^2\) and \((\sqrt{14})^2\) separately to simplify the expression.

Key Concepts

Difference of Squares

The difference of squares is a fundamental algebraic identity that states that for any two terms a and b, the expression (a - b)(a + b) equals a² - b². This concept is crucial for simplifying expressions involving square roots, as it allows us to eliminate the square roots by transforming the expression into a difference of squares.

Square Roots

Square roots are a mathematical operation that finds a number which, when multiplied by itself, gives the original number. Understanding how to simplify square roots, such as √28 and √14, is essential for performing operations involving them, especially when they appear in algebraic expressions.

Simplification of Radicals

Simplification of radicals involves reducing square roots to their simplest form, which often includes factoring out perfect squares. This process is important for making calculations easier and clearer, especially when performing operations like addition, subtraction, or multiplication of square roots.