Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √36

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Recognize that the problem involves finding the square root of 36, which is written as √36.

Recall the definition of a square root: The square root of a number is a value that, when multiplied by itself, equals the original number.

Determine if the number under the square root (36) is a perfect square. A perfect square is a number that can be expressed as the square of an integer.

Since 36 is a perfect square (6 × 6 = 36), the square root of 36 is a real number.

Conclude that the square root of 36 is the positive value of the integer that satisfies the equation x² = 36.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Square Roots

A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 36 is 6, since 6 × 6 = 36. Square roots can be both positive and negative, but in most contexts, the principal (non-negative) square root is used.

Real Numbers

Real numbers include all the numbers on the number line, encompassing rational numbers (like integers and fractions) and irrational numbers (like √2 or π). When evaluating square roots, it's important to determine if the result is a real number; for instance, the square root of a negative number is not a real number.

Evaluating Expressions

Evaluating an expression involves substituting values into the expression and simplifying it to find a numerical result. In the case of square roots, this means determining the value that satisfies the equation x² = the given number, ensuring that the result is a real number when applicable.

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