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


√3² − 4 ⋅ 2 ⋅ 5

Verified step by step guidance

1. Identify the expression to simplify: \( \sqrt{3}^2 - 4 \cdot 2 \cdot 5 \).
2. Simplify \( \sqrt{3}^2 \) by recognizing that squaring a square root cancels the square root, resulting in \( 3 \).
3. Calculate the product \( 4 \cdot 2 \cdot 5 \) by first multiplying \( 4 \cdot 2 = 8 \), and then multiplying the result by \( 5 \).
4. Subtract the result of the product from the simplified square root: \( 3 - (4 \cdot 2 \cdot 5) \).
5. Write the final expression in standard form after performing the subtraction.

Key Concepts

Square Roots

The square root of a number is a value that, when multiplied by itself, gives the original number. In this question, √3² simplifies to 3, as the square root and the square cancel each other out. Understanding square roots is essential for simplifying expressions involving powers.

Order of Operations

Order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. The acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. In this problem, it is crucial to apply these rules correctly to simplify the expression accurately.

Standard Form

Standard form in mathematics typically refers to writing numbers in a conventional way, often as a single number or a simplified expression. In the context of this problem, it means expressing the result of the simplification in a clear and concise manner, which may involve combining like terms and ensuring no further simplification is possible.