In Exercises 29–36, simplify and write the result in standard form. √(3² - 4 × 2 × 5)

검증된 단계별 안내

Start by simplifying the expression inside the square root. The expression is 3^2 - 4 × 2 × 5. First, calculate 3^2, which means 3 raised to the power of 2.

Next, calculate the product of 4, 2, and 5. Multiply these numbers together to simplify the second term inside the square root.

Subtract the result of the multiplication (4 × 2 × 5) from the result of 3^2. This will simplify the expression inside the square root to a single value.

Now, take the square root of the simplified value obtained in the previous step. Ensure that the value inside the square root is non-negative, as square roots of negative numbers are not real numbers.

Finally, write the result in standard form. If the square root simplifies to an integer, write the integer. If it does not simplify completely, leave it in simplified radical form.

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주요 개념

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

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 fundamental in algebra for solving equations and simplifying 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 common 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 under the square root accurately.

Standard Form

Standard form in mathematics typically refers to a way of writing numbers or expressions in a conventional format. For complex numbers, it is expressed as a + bi, where a and b are real numbers and i is the imaginary unit. In this context, simplifying the expression to standard form means presenting the final result clearly and concisely, which is essential for clarity in mathematical communication.

In Exercises 29–36, simplify and write the result in standard form. √(32 - 4 × 2 × 5)