Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Radical Expressions

College Algebra

0. Review of Algebra

Radical Expressions

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1:32 minutes

Problem 19

Textbook Question

In Exercises 1–20, evaluate each expression, or state that the expression is not a real number.______√16 − 25

Verified step by step guidance

Identify the expression under the square root: \( \sqrt{16} - 25 \).

Calculate the square root of 16, which is 4, so the expression becomes \( 4 - 25 \).

Subtract 25 from 4, resulting in \( -21 \).

Since the result is a negative number, check if the expression is asking for a real number.

Conclude that \( \sqrt{16} - 25 \) evaluates to \(-21\), which is a real number.

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Key Concepts

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

Square Roots

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, since 4 × 4 = 16. Understanding square roots is essential for evaluating expressions that involve radical signs.

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 evaluating expressions, it is important to determine whether the result is a real number or not, especially when dealing with square roots of negative numbers.

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 expressions like the one given.