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

검증된 단계별 안내

Recognize that the expression \((\sqrt{28} - \sqrt{14})(\sqrt{28} + \sqrt{14})\) is in the form of a difference of squares: \((a - b)(a + b) = a^2 - b^2\).

Identify \(a = \sqrt{28}\) and \(b = \sqrt{14}\) in the given expression.

Apply the difference of squares formula: \(a^2 - b^2 = (\sqrt{28})^2 - (\sqrt{14})^2\).

Simplify the squares of the square roots: \((\sqrt{28})^2 = 28\) and \((\sqrt{14})^2 = 14\).

Subtract the results to get the simplified expression: \(28 - 14\).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.