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: \(\sqrt{144} + \sqrt{25}\).
2. Recall that the square root function \(\sqrt{x}\) gives the non-negative number which, when squared, equals \(x\).
3. Calculate \(\sqrt{144}\) by finding the number that squared equals 144.
4. Calculate \(\sqrt{25}\) by finding the number that squared equals 25.
5. Add the two results together to get the value of the expression.

Key Concepts

Square Roots

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, √144 equals 12 because 12 × 12 = 144. Understanding how to find square roots is essential for evaluating expressions involving radicals.

Simplifying Radical Expressions

Simplifying radicals involves finding the principal square root and expressing the result in simplest form. When adding or subtracting square roots, only like radicals can be combined directly. In this problem, each root is simplified separately before performing addition.

Real Numbers and Roots

A real number root exists only if the radicand (the number under the root) is non-negative for even roots. If the radicand is negative, the root is not a real number. This concept helps determine whether the expression yields a real value or not.