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 expressions under the square roots: \( \sqrt{144} \) and \( \sqrt{25} \).
2. Calculate the square root of 144. Recall that the square root of a number \( x \) is a number \( y \) such that \( y^2 = x \).
3. Calculate the square root of 25. Similarly, find a number \( z \) such that \( z^2 = 25 \).
4. Add the results of the two square roots together.
5. Verify that both square roots are real numbers, as both 144 and 25 are perfect squares.

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 square roots is essential for evaluating expressions involving radical signs.

Addition of Real Numbers

In algebra, the addition of real numbers involves combining two or more numbers to obtain a sum. When evaluating expressions like √144 + √25, it is important to first calculate each square root separately before performing the addition to find the final result.

Real vs. Non-Real Numbers

Real numbers include all the numbers on the number line, encompassing both rational and irrational numbers. In contrast, non-real numbers, such as imaginary numbers, do not have a corresponding point on the number line. Recognizing whether a root is real or not is crucial when evaluating expressions that involve square roots.