In Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ___ -√ 36

Verified step by step guidance

1. Identify the expression: \(-\sqrt{36}\).
2. Recognize that \(\sqrt{36}\) represents the principal (positive) square root of 36.
3. Calculate the principal square root: \(\sqrt{36} = 6\).
4. Apply the negative sign to the result: \(-6\).
5. Conclude that the expression evaluates to a real number.

Key Concepts

Square Roots

A square root of a number 'x' is a value 'y' such that y² = x. For non-negative numbers, square roots yield real numbers. For example, the square root of 36 is 6, since 6² = 36. Understanding square roots is essential for evaluating expressions involving radical signs.

Negative Square Roots

The square root of a negative number is not defined within the set of real numbers. For instance, -√36 implies taking the square root of a negative value, which leads to an imaginary number. This concept is crucial for determining whether an expression results in a real number or not.

Real Numbers

Real numbers include all rational and irrational numbers, encompassing integers, fractions, and non-repeating decimals. They do not include imaginary or complex numbers. Recognizing whether an expression evaluates to a real number is vital for solving algebraic problems accurately.