In Exercises 1–20, evaluate each expression, or state that the expression is not a real number.______√16 − 25

Verified step by step guidance

1. Identify the expression under the square root: \( \sqrt{16} - 25 \).
2. Calculate the square root of 16, which is 4, so the expression becomes \( 4 - 25 \).
3. Subtract 25 from 4, resulting in \( -21 \).
4. Since the result is a negative number, check if the expression is asking for a real number.
5. Conclude that \( \sqrt{16} - 25 \) evaluates to \(-21\), which is a real number.

Key Concepts

Square Roots

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, since 4 × 4 = 16. Understanding square roots is essential for evaluating expressions that involve radical signs.

Real Numbers

Real numbers include all the rational and irrational numbers that can be found on the number line. This includes integers, fractions, and decimals. In the context of evaluating expressions, it is important to determine whether the result is a real number or not, especially when dealing with square roots of negative numbers.

Order of Operations

The order of operations is a set of rules that dictates the sequence in which different 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. Applying these rules correctly is crucial when evaluating expressions like the one given.