Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √25−√16

Verified step by step guidance

1. Step 1: Recognize that the problem involves square roots, which are operations that find the number that, when squared, equals the given value.
2. Step 2: Break the expression into two separate square root terms: √25 and √16.
3. Step 3: Evaluate each square root individually. For example, find the square root of 25 and the square root of 16. Recall that the square root of a number is the positive value that, when multiplied by itself, equals the original number.
4. Step 4: Subtract the result of √16 from the result of √25. Perform the subtraction operation as indicated in the expression.
5. Step 5: Verify that the result is a real number. Since both √25 and √16 are real numbers, their difference will also be a real number.

Key Concepts

Square Roots

A square root of a number 'x' is a value 'y' such that y² = x. For example, the square root of 25 is 5 because 5² = 25. Square roots can be both positive and negative, but in most contexts, the principal (non-negative) square root is used. Understanding how to calculate square roots is essential for evaluating expressions involving them.

Real Numbers

Real numbers include all the numbers on the number line, encompassing rational numbers (like integers and fractions) and irrational numbers (like √2). When evaluating expressions, 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, which is a key consideration in algebra.

Simplifying Expressions

Simplifying expressions involves reducing them to their simplest form, which often includes combining like terms and performing operations such as addition, subtraction, multiplication, and division. In the context of the given expression, √25 - √16, simplifying requires calculating the square roots first and then performing the subtraction, leading to a clearer understanding of the result.