In Exercises 29–36, simplify and write the result in standard form. √(3^2 - 4 × 2 × 5)

Verified step by step guidance

1. Identify the expression inside the square root: \(3^2 - 4 \times 2 \times 5\).
2. Calculate \(3^2\), which is \(9\).
3. Calculate \(4 \times 2 \times 5\), which is \(40\).
4. Subtract the result of the multiplication from the square: \(9 - 40\).
5. Simplify the expression under the square root and write the result in standard form.

Key Concepts

Square Root

The square root of a number is a value that, when multiplied by itself, gives the original number. In this problem, we need to simplify the expression under the square root before calculating its value. The square root is denoted by the radical symbol (√) and is essential for solving equations involving quadratic expressions.

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 exercise, correctly applying these rules is crucial for simplifying the expression accurately.

Standard Form

Standard form in mathematics typically refers to expressing numbers in a conventional way, such as writing a polynomial in descending order of its degree or representing complex numbers as a + bi. In this context, simplifying the square root expression and presenting the final result in standard form is important for clarity and consistency in mathematical communication.