In Exercises 29–36, simplify and write the result in standard form.

√3² − 4 ⋅ 2 ⋅ 5

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Identify the expression given: \(\sqrt{3}^2 - 4 \cdot 2 \cdot 5\).

Simplify the square of the square root: \(\left(\sqrt{3}\right)^2 = 3\) because squaring a square root cancels out the root.

Calculate the product in the second term: multiply \(4\), \(2\), and \(5\) together to get \(4 \cdot 2 \cdot 5\).

Rewrite the expression with the simplified parts: \(3 - (4 \cdot 2 \cdot 5)\).

Perform the subtraction to write the expression in its simplest standard form.

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주요 개념

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Order of Operations

The order of operations dictates the sequence in which mathematical operations are performed to ensure consistent results. It follows the PEMDAS/BODMAS rules: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). Applying this correctly is essential to simplify expressions accurately.

Square Roots and Exponents

Understanding how to handle square roots and exponents is crucial. The square root of a number is a value that, when squared, gives the original number. Squaring a square root (e.g., (√3)²) simplifies back to the original number (3), which helps in simplifying expressions involving radicals.

Simplifying Algebraic Expressions

Simplifying algebraic expressions involves combining like terms and performing arithmetic operations to write the expression in its simplest form. This includes evaluating products, sums, and differences, and rewriting the result in a standard or canonical form for clarity and further use.

In Exercises 29–36, simplify and write the result in standard form.√3² − 4 ⋅ 2 ⋅ 5