Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √144+25

Verified step by step guidance

1. Identify the expression to evaluate: \( \sqrt{144} + 25 \).
2. Calculate the square root of 144. Recall that \( \sqrt{144} = 12 \) because 12 multiplied by itself equals 144.
3. Substitute the value of \( \sqrt{144} \) with 12 in the expression.
4. Add the result from the square root calculation to 25.
5. The expression simplifies to the sum of 12 and 25.

Key Concepts

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 144 is 12, since 12 × 12 = 144. Understanding how to calculate square roots is essential for evaluating expressions that involve them.

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 square roots, it's important to recognize that the square root of a negative number is not a real number, which is a key consideration when evaluating expressions.

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 complex expressions.