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 difference of squares: \((a - b)(a + b) = a^2 - b^2\).
2. Identify \(a = \sqrt{28}\) and \(b = \sqrt{14}\) in the given expression.
3. Apply the difference of squares formula: \(a^2 - b^2 = (\sqrt{28})^2 - (\sqrt{14})^2\).
4. Simplify the squares of the square roots: \((\sqrt{28})^2 = 28\) and \((\sqrt{14})^2 = 14\).
5. Subtract the results to get the simplified expression: \(28 - 14\).

Key Concepts

Difference of Squares Formula

The difference of squares formula states that (a - b)(a + b) = a² - b². This identity allows simplification of expressions involving the product of conjugates without expanding each term individually.

Simplifying Square Roots

Simplifying square roots involves expressing the radicand as a product of perfect squares and other factors, making it easier to perform arithmetic operations or further simplifications.

Mental Math Strategies in Algebra

Mental math strategies help perform calculations quickly by recognizing patterns or formulas, such as the difference of squares, enabling one to avoid lengthy intermediate steps.